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Important polynomial time computational problems on DAGs include topological sorting ( finding a topological ordering ) , construction of the transitive closure and transitive reduction ( the largest and smallest DAGs with the same reachability relation , respectively ) , and the closure problem , in which the goal is to find a minimum @-@ weight subset of vertices with no edges connecting them to the rest of the graph . Transforming a directed graph with cycles into a DAG by deleting as few vertices or edges as possible ( the feedback vertex set and feedback edge set problem , respectively ) is NP @-@ hard , but any directed graph can be made into a DAG ( its condensation ) by contracting each strongly connected component into a single supervertex . The problems of finding shortest paths and longest paths can be solved on DAGs in linear time , in contrast to arbitrary graphs for which shortest path algorithms are slower and longest path problems are NP @-@ hard . |
The corresponding concept for undirected graphs is a forest , an undirected graph without cycles . Choosing an orientation for a forest produces a special kind of directed acyclic graph called a polytree . However there are many other kinds of directed acyclic graph that are not formed by orienting the edges of an undirected acyclic graph . Moreover , every undirected graph has an acyclic orientation , an assignment of a direction for its edges that makes it into a directed acyclic graph . To emphasize that DAGs are not the same thing as directed versions of undirected acyclic graphs , some authors call them acyclic directed graphs or acyclic digraphs . |
= = Definitions = = |
A graph is formed by a collection of vertices and edges , where the vertices are structureless objects that are connected in pairs by edges . In the case of a directed graph , each edge has an orientation , from one vertex to another vertex . A path in a directed graph can be described by a sequence of edges having the property that the ending vertex of each edge in the sequence is the same as the starting vertex of the next edge in the sequence ; a path forms a cycle if the starting vertex of its first edge equals the ending vertex of its last edge . A directed acyclic graph is a directed graph that has no cycles . |
A vertex v of a directed graph is said to be reachable from another vertex u when there exists a path that starts at u and ends at v. As a special case , every vertex is considered to be reachable from itself ( by a path with zero edges ) . If a vertex can reach itself via a nontrivial path ( a path with one or more edges ) , then that path is a cycle , so another way to define directed acyclic graphs is that they are the graphs in which no vertex can reach itself via a nontrivial path . |
A topological ordering of a directed graph is an ordering of its vertices into a sequence , such that for every edge the start vertex of the edge occurs earlier in the sequence than the ending vertex of the edge . A graph that has a topological ordering cannot have any cycles , because the edge into the earliest vertex of a cycle would have to be oriented the wrong way . Therefore , every graph with a topological ordering is acyclic . Conversely , every directed acyclic graph has a topological ordering . Therefore , this property can be used as an alternative definition of the directed acyclic graphs : they are exactly the graphs that have topological orderings . |
= = Mathematical properties = = |
= = = Reachability , transitive closure , and transitive reduction = = = |
The reachability relationship in any directed acyclic graph can be formalized as a partial order ≤ on the vertices of the DAG . In this partial order , two vertices u and v are ordered as u ≤ v exactly when there exists a directed path from u to v in the DAG ; that is , when v is reachable from u . However , different DAGs may give rise to the same reachability relation and the same partial order . For example , the DAG with two edges a → b and b → c has the same reachability relation as the graph with three edges a → b , b → c , and a → c . Both of these DAGS produce the same partial order , in which the vertices are ordered as a ≤ b ≤ c . |
If G is a DAG , its transitive closure is the graph with the most edges that represents the same reachability relation . It has an edge u → v whenever u can reach v. That is , it has an edge for every related pair u ≤ v of distinct elements in the reachability relation of G , and may therefore be thought of as a direct translation of the reachability relation ≤ into graph @-@ theoretic terms . The same method of translating partial orders into DAGs works more generally : for every finite partially ordered set ( S , ≤ ) , the graph that has a vertex for each member of S and an edge for each pair of elements related by u ≤ v is automatically a transitively closed DAG , and has ( S , ≤ ) as its reachability relation . In this way , every finite partially ordered set can be represented as the reachability relation of a DAG . |
The transitive reduction of a DAG G is the graph with the fewest edges that represents the same reachability relation as G. It is a subgraph of G , formed by discarding the edges u → v for which G also contains a longer path connecting the same two vertices . Like the transitive closure , the transitive reduction is uniquely defined for DAGs . In contrast , for a directed graph that is not acyclic , there can be more than one minimal subgraph with the same reachability relation . |
If a DAG G has a reachability relation described by the partial order ≤ , then the transitive reduction of G is a subgraph of G that has an edge u → v for every pair in the covering relation of ≤ . Transitive reductions are useful in visualizing the partial orders they represent , because they have fewer edges than other graphs representing the same orders and therefore lead to simpler graph drawings . A Hasse diagram of a partial order is a drawing of the transitive reduction in which the orientation of each edge is shown by placing the starting vertex of the edge in a lower position than its ending vertex . |
= = = Topological ordering = = = |
Every directed acyclic graph has a topological ordering , an ordering of the vertices such that the starting endpoint of every edge occurs earlier in the ordering than the ending endpoint of the edge . The existence of such an ordering can be used to characterize DAGs : a directed graph is a DAG if and only if it has a topological ordering . In general , this ordering is not unique ; a DAG has a unique topological ordering if and only if it has a directed path containing all the vertices , in which case the ordering is the same as the order in which the vertices appear in the path . |
The family of topological orderings of a DAG is the same as the family of linear extensions of the reachability relation for the DAG , so any two graphs representing the same partial order have the same set of topological orders . |
= = = Combinatorial enumeration = = = |
The graph enumeration problem of counting directed acyclic graphs was studied by Robinson ( 1973 ) . The number of DAGs on n labeled vertices , for n = 0 , 1 , 2 , 3 , … ( without restrictions on the order in which these numbers appear in a topological ordering of the DAG ) is |
1 , 1 , 3 , 25 , 543 , 29281 , 3781503 , … ( sequence A003024 in the OEIS ) . |
These numbers may be computed by the recurrence relation |
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Eric W. Weisstein conjectured , and McKay et al . ( 2004 ) proved , that the same numbers count the ( 0 @,@ 1 ) matrices for which all eigenvalues are positive real numbers . The proof is bijective : a matrix A is an adjacency matrix of a DAG if and only if A + I is a ( 0 @,@ 1 ) matrix with all eigenvalues positive , where I denotes the identity matrix . Because a DAG cannot have self @-@ loops , its adjacency matrix must have a zero diagonal , so adding I preserves the property that all matrix coefficients are 0 or 1 . |
= = = Related families of graphs = = = |
A polytree is a directed graph formed by orienting the edges of a free tree . Every polytree is a DAG . In particular , this is true of the arborescences formed by directing all edges outwards from the roots of a tree . |
A multitree ( also called a strongly unambiguous graph or a mangrove ) is a directed graph in which there is at most one directed path ( in either direction ) between any two vertices ; equivalently , it is a DAG in which , for every vertex v , the subgraph reachable from v forms a tree . |
= = Computational problems = = |
= = = Topological sorting and recognition = = = |
Topological sorting is the algorithmic problem of finding a topological ordering of a given DAG . It can be solved in linear time . Kahn 's algorithm for topological sorting builds the vertex ordering directly . It maintains a list of vertices that have no incoming edges from other vertices that have not already been included in the partially constructed topological ordering ; initially this list consists of the vertices with no incoming edges at all . Then , it repeatedly adds one vertex from this list to the end of the partially constructed topological ordering , and checks whether its neighbors should be added to the list . The algorithm terminates when all vertices have been processed in this way . Alternatively , a topological ordering may be constructed by reversing a postorder numbering of a depth @-@ first search graph traversal . |
It is also possible to check whether a given directed graph is a DAG in linear time , either by attempting to find a topological ordering and then testing for each edge whether the resulting ordering is valid or alternatively , for some topological sorting algorithms , by verifying that the algorithm successfully orders all the vertices without meeting an error condition . |
= = = Construction from cyclic graphs = = = |
Any undirected graph may be made into a DAG by choosing a total order for its vertices and directing every edge from the earlier endpoint in the order to the later endpoint . The resulting orientation of the edges is called an acyclic orientation . Different total orders may lead to the same acyclic orientation , so an n @-@ vertex graph can have fewer than n ! acyclic orientations . The number of acyclic orientations is equal to | χ ( − 1 ) | , where χ is the chromatic polynomial of the given graph . |
Any directed graph may be made into a DAG by removing a feedback vertex set or a feedback arc set , a set of vertices or edges ( respectively ) that touches all cycles . However , the smallest such set is NP @-@ hard to find . An arbitrary directed graph may also be transformed into a DAG , called its condensation , by contracting each of its strongly connected components into a single supervertex . When the graph is already acyclic , its smallest feedback vertex sets and feedback arc sets are empty , and its condensation is the graph itself . |
= = = Transitive closure and transitive reduction = = = |
The transitive closure of a given DAG , with n vertices and m edges , may be constructed in time O ( mn ) by using either breadth @-@ first search or depth @-@ first search to test reachability from each vertex . Alternatively , it can be solved in time O ( nω ) where ω < 2 @.@ 373 is the exponent for fast matrix multiplication algorithms ; this is a theoretical improvement over the O ( mn ) bound for dense graphs . |
In all of these transitive closure algorithms , it is possible to distinguish pairs of vertices that are reachable by at least one path of length two or more from pairs that can only be connected by a length @-@ one path . The transitive reduction consists of the edges that form length @-@ one paths that are the only paths connecting their endpoints . Therefore , the transitive reduction can be constructed in the same asymptotic time bounds as the transitive closure . |
= = = Closure problem = = = |
The closure problem takes as input a directed acyclic graph with weights on its vertices and seeks the minimum ( or maximum ) weight of a closure , a set of vertices with no outgoing edges . ( The problem may be formulated for directed graphs without the assumption of acyclicity , but with no greater generality , because in this case it is equivalent to the same problem on the condensation of the graph . ) It may be solved in polynomial time using a reduction to the maximum flow problem . |
= = = Path algorithms = = = |
Some algorithms become simpler when used on DAGs instead of general graphs , based on the principle of topological ordering . For example , it is possible to find shortest paths and longest paths from a given starting vertex in DAGs in linear time by processing the vertices in a topological order , and calculating the path length for each vertex to be the minimum or maximum length obtained via any of its incoming edges . In contrast , for arbitrary graphs the shortest path may require slower algorithms such as Dijkstra 's algorithm or the Bellman – Ford algorithm , and longest paths in arbitrary graphs are NP @-@ hard to find . |
= = Applications = = |
= = = Scheduling = = = |
Directed acyclic graphs representations of partial orderings have many applications in scheduling for systems of tasks with ordering constraints . An important class of problems of this type concern collections of objects that need to be updated , such as the cells of a spreadsheet after one of the cells has been changed , or the object files of a piece of computer software after its source code has been changed . In this context , a dependency graph is a graph that has a vertex for each object to be updated , and an edge connecting two objects whenever one of them needs to be updated earlier than the other . A cycle in this graph is called a circular dependency , and is generally not allowed , because there would be no way to consistently schedule the tasks involved in the cycle . Dependency graphs without circular dependencies form DAGs . |
For instance , when one cell of a spreadsheet changes , it is necessary to recalculate the values of other cells that depend directly or indirectly on the changed cell . For this problem , the tasks to be scheduled are the recalculations of the values of individual cells of the spreadsheet . Dependencies arise when an expression in one cell uses a value from another cell . In such a case , the value that is used must be recalculated earlier than the expression that uses it . Topologically ordering the dependency graph , and using this topological order to schedule the cell updates , allows the whole spreadsheet to be updated with only a single evaluation per cell . Similar problems of task ordering arise in makefiles for program compilation and instruction scheduling for low @-@ level computer program optimization . |
A somewhat different DAG @-@ based formulation of scheduling constraints is used by the program evaluation and review technique ( PERT ) , a method for management of large human projects that was one of the first applications of DAGs . In this method , the vertices of a DAG represent milestones of a project rather than specific tasks to be performed . Instead , a task or activity is represented by an edge of a DAG , connecting two milestones that mark the beginning and completion of the task . Each such edge is labeled with an estimate for the amount of time that it will take a team of workers to perform the task . The longest path in this DAG represents the critical path of the project , the one that controls the total time for the project . Individual milestones can be scheduled according to the lengths of the longest paths ending at their vertices . |
= = = Data processing networks = = = |
A directed acyclic graph may be used to represent a network of processing elements . In this representation , data enters a processing element through its incoming edges and leaves the element through its outgoing edges . |
For instance , in electronic circuit design , static combinational logic blocks can be represented as an acyclic system of logic gates that computes a function of an input , where the input and output of the function are represented as individual bits . In general , the output of these blocks cannot be used as the input unless it is captured by a register or state element which maintains its acyclic properties . Electronic circuit schematics either on paper or in a database are a form of directed acyclic graphs using instances or components to form a directed reference to a lower level component . Electronic circuits themselves are not necessarily acyclic or directed . |
Dataflow programming languages describe systems of operations on data streams , and the connections between the outputs of some operations and the inputs of others . These languages can be convenient for describing repetitive data processing tasks , in which the same acyclically @-@ connected collection of operations is applied to many data items . They can be executed as a parallel algorithm in which each operation is performed by a parallel process as soon as another set of inputs becomes available to it . |
In compilers , straight line code ( that is , sequences of statements without loops or conditional branches ) may be represented by a DAG describing the inputs and outputs of each of the arithmetic operations performed within the code . This representation allows the compiler to perform common subexpression elimination efficiently . |
= = = Causal structures = = = |
Graphs that have vertices representing events , and edges representing causal relations between events , are often acyclic – arranging the vertices in linear order of time , all arrows point in the same direction as time , from parent to child ( due to causality affecting the future , not the past ) , and thus have no loops . |
For instance , a Bayesian network represents a system of probabilistic events as vertices in a directed acyclic graph , in which the likelihood of an event may be calculated from the likelihoods of its predecessors in the DAG . In this context , the moral graph of a DAG is the undirected graph created by adding an ( undirected ) edge between all parents of the same vertex ( sometimes called marrying ) , and then replacing all directed edges by undirected edges . |
Another type of graph with a similar causal structure is an influence diagram , the vertices of which represent either decisions to be made or unknown information , and the edges of which represent causal influences from one vertex to another . In epidemiology , for instance , these diagrams are often used to estimate the expected value of different choices for intervention . |
= = = Genealogy and version history = = = |
Family trees may be seen as directed acyclic graphs , with a vertex for each family member and an edge for each parent @-@ child relationship . Despite the name , these graphs are not necessarily trees because of the possibility of marriages between relatives ( so a child has a common ancestor on both the mother 's and father 's side ) causing pedigree collapse . The graphs of matrilineal descent ( " mother " relationships between women ) and patrilineal descent ( " father " relationships between men ) are trees within this graph . Because no one can become their own ancestor , family trees are acyclic . |
For the same reason , the version history of a distributed revision control system generally has the structure of a directed acyclic graph , in which there is a vertex for each revision and an edge connecting pairs of revisions that were directly derived from each other . These are not trees in general due to merges . |
In many randomized algorithms in computational geometry , the algorithm maintains a history DAG representing the version history of a geometric structure over the course of a sequence of changes to the structure . For instance in a randomized incremental algorithm for Delaunay triangulation , the triangulation changes by replacing one triangle by three smaller triangles when each point is added , and by " flip " operations that replace pairs of triangles by a different pair of triangles . The history DAG for this algorithm has a vertex for each triangle constructed as part of the algorithm , and edges from each triangle to the two or three other triangles that replace it . This structure allows point location queries to be answered efficiently : to find the location of a query point q in the Delaunay triangulation , follow a path in the history DAG , at each step moving to the replacement triangle that contains q . The final triangle reached in this path must be the Delaunay triangle that contains q . |
= = = Data compression = = = |
Directed acyclic graphs may also be used as a compact representation of a collection of sequences . In this type of application , one finds a DAG in which the paths form the given sequences . When many of the sequences share the same subsequences , these shared subsequences can be represented by a shared part of the DAG , allowing the representation to use less space than it would take to list out all of the sequences separately . For example , the directed acyclic word graph is a data structure in computer science formed by a directed acyclic graph with a single source and with edges labeled by letters or symbols ; the paths from the source to the sinks in this graph represent a set of strings , such as English words . Any set of sequences can be represented as paths in a tree , by forming a tree vertex for every prefix of a sequence and making the parent of one of these vertices represent the sequence with one fewer element ; the tree formed in this way for a set of strings is called a trie . A directed acyclic word graph saves space over a trie by allowing paths to diverge and rejoin , so that a set of words with the same possible suffixes can be represented by a single tree vertex . |
The same idea of using a DAG to represent a family of paths occurs in the binary decision diagram , a DAG @-@ based data structure for representing binary functions . In a binary decision diagram , each non @-@ sink vertex is labeled by the name of a binary variable , and each sink and each edge is labeled by a 0 or 1 . The function value for any truth assignment to the variables is the value at the sink found by following a path , starting from the single source vertex , that at each non @-@ sink vertex follows the outgoing edge labeled with the value of that vertex 's variable . Just as directed acyclic word graphs can be viewed as a compressed form of tries , binary decision diagrams can be viewed as compressed forms of decision trees that save space by allowing paths to rejoin when they agree on the results of all remaining decisions . |
= August ( Fringe ) = |
" August " is the eighth episode of the American science fiction drama television series Fringe 's second season . The episode was co @-@ written by J. H. Wyman and Jeff Pinkner , and directed by Dennis Smith . The episode marked the first prominent appearance of more than one Observer , and follows the events that occur when one of them saves a girl from boarding a soon @-@ to @-@ be crashing plane . It featured two new guest stars , Peter Woodward and Eugene Lipinski . |
The episode first aired on November 19 , 2009 in the United States to mostly positive reviews , with many critics praising the new revelations about the Observers . An estimated 5 @.@ 746 million viewers watched the episode on its first broadcast . |
= = Plot = = |
An Observer , " August " ( Peter Woodward ) abducts Christine Hollis ( Jennifer Missoni ) , a 27 @-@ year @-@ old art student in Boston . Olivia Dunham ( Anna Torv ) and Peter Bishop ( Joshua Jackson ) learn of the events and realize the assailant matches the description of the Observer . However , after viewing video footage they find that it is not " September " ( Michael Cerveris ) , the Observer known for observing Pattern @-@ related cases and who previously saved Peter and his father Walter ( John Noble ) in 1985 , indicating there is more than one Observer . Olivia is confused as to August 's motives , as Observers are known to only observe events and not interfere with them . After questioning Christine 's roommate , Olivia learns she was to take a flight to Rome , Italy . Peter finds a picture of Christine from her childhood before her parents were killed in the 1989 San Francisco earthquake , and sees August in the background , indicating he has been observing her entire life . The plane to Rome would later crash , killing everyone on board . Because of this , the team realize August in fact saved her life . |
At Massive Dynamic , Brandon ( Ryan McDonald ) theorizes to the team that Observers are time travelers , as they have been documented during several major events in history . They write in an incomprehensible language , and the number of Observer sightings has increased over the past few months , leaving the team wondering why . Meanwhile , August visits the other Observers , who are not happy that he saved a girl who was supposed to die in the plane crash . To correct his mistake , they send Donald Long ( Paul Rae ) , an assassin affiliated with the Observers to correct August 's actions . In an attempt to save Christine , August sends a secret message to Walter . During the meeting , August reveals Christine will die because she is not important ; Walter tells August that he has to make her important . |
The team are later made aware of Christine 's location at a motel outside the city . However , Donald is on the trail also . August attempts to stop him , but Donald shoots him several times , before Peter and Olivia arrive to kill the assassin . September picks up August and while driving , September asks August why he saved Christine . August reveals that he is experiencing ' feelings ' and that he loves Christine , and asks if she would be safe . September informs him Christine will stay alive because she is now important ; she was responsible for the death of an Observer . August cries before succumbing to his wounds . In the end , Olivia takes a day off to spend time with her niece , Ella , at an amusement park . Two Observers watch the two , and they remark that everything is about to get " so hard " for Olivia . |
= = Production = = |
" August " was co @-@ written by co @-@ showrunners J. H. Wyman and Jeff Pinkner , while being directed by NCIS veteran Dennis Smith . They began shooting the episode during the second half of September 2009 , right after wrapping production on " Of Human Action " . Supervising producer Josh Singer later noted how " August " helped them write the rest of the season , " There was one episode , ' August ' , which was all about the Observers , that I feel was mythology without being mythology . And somehow , in working that episode , we sort of found a new creative vein . And it 's not that that episode was necessarily so related to everything else we did . But I feel like it sort of opened us up in terms of how we were feeling about the year " . |
Up to the point the episode " August " aired , only one character that was part of a group known as " Observers " had been introduced . In this episode , two more such individuals were revealed : August ( played by Peter Woodward ) and December ( played by Eugene Lipinski ) . The creation of Observers was one of the first ideas the writers of Fringe thought of when developing the show in its early stages , when they asked each other , " What if there were these characters where all they did was watch ? " . Pinkner and Wyman thought of creating Observers by " looking for something ... iconic " that had the " quality of being invisible " . Though the Observer called September has appeared in every single Fringe episode in a brief cameo , he was first featured prominently in the fourth episode of the first season . The producers thought of unique characteristics for " somebody who wasn 't of our world , " evolving to the Observers having bald heads , no eyebrows , and " largely deadened " senses , which led to a love for extremely hot peppers . |
Before the second season premiere aired in September 2009 , co @-@ creator J.R. Orci hinted that the audience was going to meet " many Observers " , and that in the season 's eighth episode , " You 're going to find out their role in the world , what they 're named after , and their connection to some of these characters . " Later on , when still leading up to the airing of " August " in another interview , Roberto Orci elaborated that " Individuality will be one of the things that they will be fanatically struggling with , actually . That was a fun one , because that one was one where you 're finally getting to pay off things you 've been setting up for a year . You finally get to open the toy box and really play with those toys " . Actor Michael Cerveris , who plays September , commented in an interview that as a result of the episode , viewers would learn that the Observers " are not completely devoid of feelings , and are not incapable of being attached to people they 're observing " . He also expressed relief that his character was no longer the sole Observer on the show , joking that " it was nice to feel like I 'm not the only freak in town for once " . |
Actress Anna Torv stated in an interview with MTV News that " August " was one of her favorite episodes because " We sort of get to meet the Observers . At the moment what we know about them , they ... seemingly just observe . That 's kind of it , but [ in ] the episode that we have coming up , we 're not sure if all they do is just observe " . |
= = Reception = = |
= = = Ratings = = = |
" August " premiered to an estimated 5 @.@ 746 million viewers in the United States , with a 2 @.@ 0 rating . The episode was down 9 % from the previous week 's episode " Of Human Action " , which had a rating of 2 @.@ 2 . |
= = = Reviews = = = |
MTV 's Josh Wigler thought the episode was " a touching , sad tale with a healthy mix of mythological advancement , " and couldn 't wait for more episodes about the Observers . Ramsey Isler of IGN gave the episode 7 @.@ 6 / 10 , writing that despite the hype , the episode was " just plain average " . He did however appreciate the new revelations about the Observers . After previewing the episode , Entertainment Weekly 's Ken Tucker graded the episode an A- , explaining Fringe had become " one of the fastest , smartest , wittiest shows on television now " . Andrew Hanson from the Los Angeles Times called it a " good story peppered with a lot of great details ... ' August ' showed a greater connection to the larger Fringe universe " . Noel Murray of The A.V. Club graded it with a B + , praising the " wonderfully moody " episode and how it was able to make the halting Observer dialogue work . Murray found some aspects lacking however , as he thought it was " a very sketchy episode , plot @-@ wise and mythology @-@ wise . Not a whole lot happened " . Website blogger io9 listed " August " as one of the " crucial " episodes new viewers must watch to get into the show . |
= Ghost in the Shell ( 1995 film ) = |
Ghost in the Shell , known in Japan as Mobile Armored Riot Police : Ghost In The Shell ( 攻殻機動隊 GHOST IN THE SHELL , Kōkaku Kidōtai Gōsuto In Za Sheru ) , is a 1995 science fiction anime film based on manga of the same title by Masamune Shirow . The film was written by Kazunori Itō , directed by Mamoru Oshii , animated by Production I.G , and starred the voices of Atsuko Tanaka , Akio Ōtsuka , and Iemasa Kayumi . |
Ghost in the Shell follows the hunt by the public @-@ security agency Section 9 for a mysterious hacker known as the Puppet Master . With the assistance of her team , Motoko Kusanagi tracks and finds their suspect , only to be drawn into a complex sequence of political intrigue and a cover @-@ up as to the identity and goals of the Puppet Master . |
The overarching philosophical themes of the film include self @-@ identity in a technologically advanced world . The music , composed by Kenji Kawai , included an ancient Japanese language in a wedding song that serves as a key piece of music leading up to the climax of the movie . Widely considered one of the greatest anime films of all time , critics particularly praised its visuals , which at the time were the most effective synthesis of traditional cel animation and CG animation . It has served as inspiration for filmmakers such as the Wachowskis . |
In 2004 , Oshii directed Ghost in the Shell 2 : Innocence , billed as a separate work and not a true sequel . In 2008 , Oshii released an updated version of the original film , Ghost in the Shell 2 @.@ 0 , that features new audio and updated 3D animation . A live @-@ action Hollywood Ghost in the Shell remake is scheduled for 2017 . |
= = Plot = = |
In 2029 , the world is interconnected by a vast electronic network that permeates every aspect of life . Much of humanity has access to this network through cybernetic bodies , or " shells " , which possess their consciousness and can give them superhuman abilities . |
Major Motoko Kusanagi , an assault @-@ team leader for the Public Security Section 9 , is assigned to capture an elusive hacker known as the Puppet Master . Her team , Batou and Ishikawa , use triangulation to seek out the Puppet Master . Their suspect is a garbageman who believes he is using a program obtained from a sympathetic man to illegally " ghost @-@ hack " his wife 's mind to find his daughter . Kusanagi and her team arrest him and the man who gave him the program , but discover that their memories were either erased or implanted : " ghost @-@ hacked " by the Puppet Master . |
A facility is hacked and programmed to assemble a female cybernetic body . The body escapes but is hit by a truck ; Section 9 investigates and examines the body , which seems to have a human " ghost " inside — perhaps the Puppet Master himself . Officials from rival agency Section 6 visit Section 9 and explain that the body was made to lure the Puppet Master 's ghost and trap it inside . Kusanagi espies the conversation and decides to disconnect her consciousness from her current body and connect or " dive into " the body and face the Puppet Master 's ghost . Before she succeeds , the ghost activates the body . Section 6 storms Section 9 and reclaims the body . |
The information from the body leads Section 9 to uncover the mysterious Project 2501 . Section 6 claims the project was created to catch the hacker , but it was initiated before his appearance . Section 9 speculates that the project itself created the Puppet Master , who then escaped , and Section 6 now wants him back . Daisuke Aramaki , head of Section 9 , suspects that the project and the Puppet Master are tools of the Ministry of Foreign Affairs . The escape might lead to the release of secrets that could embarrass Section 6 and the Ministry . |
The getaway car carrying the Puppet Master meets another , and they split off . Batou stops the first car and realizes it is a decoy . Kusanagi follows the second car to an abandoned building , where she is ambushed by a spider @-@ like armored vehicle . Batou arrives in time to save the badly damaged Kusanagi . With Batou on guard , Kusanagi faces the body stolen by Section 6 . The Puppet Master reveals himself and explains that , under Project 2501 , he was created by Section 6 to hack ghosts for individuals and Section 6 . While wandering various networks , the Puppet Master became sentient and began to contemplate his existence ; it troubled him that he could not reproduce or die . He plans to merge with Kusanagi 's ghost to experience mortality ; Kusanagi would live on with his ghost . As he could not crack Section 6 's attack protection , he was forced to escape in a physical body . |
Batou tries to disconnect the dive , but the Puppet Master ghost @-@ hacks him . Helicopters from Section 6 arrive with orders to destroy everyone inside to cover up Project 2501 . The Puppet Master disrupts their targeting systems . As he starts merging with Kusanagi , snipers blow their heads off , along with Batou 's arm . |
Kusanagi wakes up in a child @-@ sized cyborg body in Batou 's safehouse . Batou explains that her original body was destroyed in the fight ; he recovered her head and attached it to the new body . Kusanagi acknowledges she is now neither herself nor the Puppet Master , but a combination of both . Batou says he will always be there for her . She leaves the house and gazes out over the city . |
= = Voice cast = = |
= = Production = = |
= = = Development = = = |
Director Mamoru Oshii stated , " My intuition told me that this story about a futuristic world carried an immediate message for our present world . I am also interested in computers through my own personal experience with them . I had the same feeling about Patlabor and I thought it would be interesting to make a film that took place in the near future . There are only a few movies , even out of Hollywood , which clearly portray the influence and power of computers . I thought this theme would be more effectively conveyed through animation . " Oshii expanded on these thoughts in a later interview , noting that technology changes people and had become a part of the culture of Japan . He commented that his use of philosophy caused producers to become frustrated because of sparing use of action scenes . Oshii also acknowledged that a movie with more action would sell better , but he continued to make these movies anyway . When Oshii went back to make changes to the original Ghost in the Shell to re @-@ release it as Ghost in the Shell 2 @.@ 0 , one of the reasons he gave was that the film did not resemble the sequel . He wanted to update the film to reflect changes in perspective . |
= = = Design = = = |
Hiroyuki Okiura , the character designer and key animation supervisor , designed a more mature and serious Motoko than Masamune Shirow 's original portrayal of the character in the manga . Okiura chose to depict a physically mature person to match Motoko 's mental age , instead of the youthful twenty @-@ something appearance in the manga . Motoko 's demeanor lacks the comedic facial expressions and rebellious nature depicted in the manga . |
Oshii based the setting for Ghost in the Shell on Hong Kong . Oshii commented that his first thought to find an image of the future setting was an Asian city , but finding a suitable cityscape of the future would be impossible . Oshii chose to use the real streets of Hong Kong as his model . He also said that Hong Kong was the perfect subject and theme for the film with its countless signs and the cacophony of sounds . The film 's mecha designer Takeuchi Atsushi noted that while the film does not have a chosen setting , it is obviously based on Hong Kong because the city represented the theme of the film , the old and the new which exist in a strange relationship in an age of an information deluge . Before shooting the film , the artists drew sketches that emphasized Hong Kong 's chaotic , confusing and overwhelming aspects . |
The Hong Kong setting is alluded to by the scene wherein the characters are drinking San Miguel Beer a cultural staple of the East Asian megalopolis . |
= = = Animation = = = |
Ghost in the Shell used a novel process called " digitally generated animation " ( DGA ) , which is a combination of cel animation , computer graphics ( CG ) , and audio that is entered as digital data . In 1995 , DGA was thought to be the future of animation , which mixed traditional animation with the emerging use of computer graphics , including digital cel work with visual displays . Editing was performed on an AVID system of Avid Technology , which was chosen because it was more versatile and less limiting than other methods and worked with the different types of media in a single environment . |
The digital cel work included both original illustrations , compositions and manipulation with traditional cel animation to create a sense of depth and evoke emotion and feelings . Utilized as background , filters like a lens effect were used to create a sense of depth and motion , by distorting the front background and making the far background out of focus throughout the shot . Ghost in the Shell used a unique lighting system in which light and darkness were integrated into the cels with attention to light and shadow sources instead of using contrast to control the light . Hiromasa Ogura , the art director , described this as " a very unusual lighting technique . " |
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