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Lower and upper bounds of shortest paths in reachability graphs

P. K. Mishra
2004 International Journal of Mathematics and Mathematical Sciences  
If the Petri net is a marked graph, then the length of the shortest path is at most(|T|−1)⋅|T|/2. If the Petri net is conflict free, then the length of the shortest path is at most(|T|+1)⋅|T|/2.  ...  If the petrinet is live and extended free choice, then the length of the shortest path is at most|T|⋅|T+1|⋅|T+2|/6, whereTis the set of transitions of the net.  ...  Furthermore, we have shown that in the case of safe conflict-free systems and safe marked graphs, the bound is reachable and that the length of the shortest paths in safe persistent systems can be exponential  ... 
doi:10.1155/s0161171204403378 fatcat:5xpbytcswnaehj3gracgpcwvs4

Subgoal Graphs for Fast Optimal Pathfinding [chapter]

Tansel Uras, Sven Koenig
2015 Game AI Pro 2  
In this paper, we propose a method for preprocessing eightneighbor grids to generate subgoal graphs and show how subgoal graphs can be used to find shortest paths fast.  ...  subgoals that are easily reachable from one another.  ...  We add edges between subgoals that are direct-h-reachable from one another, resulting in a simple subgoal graph. These edges are sufficient for finding shortest paths and easy to follow.  ... 
doi:10.1201/b18373-19 fatcat:fxsxh7u3ond6lhi5b37j62tjg4

AORM: Fast Incremental Arbitrary-Order Reachability Matrix Computation for Massive Graphs

Sung-Soo Kim, Young-Kuk Kim, Young-Min Kang
2021 IEEE Access  
INDEX TERMS Reachability query, approximate all-pairs shortest paths, graph girth, graph embedding, higher-order structural proximity. 69540 VOLUME 9, 2021  ...  In particular, the proposed method outperforms up to 10 times compared to NetworkX for incremental allpairs shortest paths computation.  ...  These benefits include fundamental operations in graph embedding, such as capturing arbitrary-order proximity, computing allpairs shortest paths, and processing reachability queries in a graph.  ... 
doi:10.1109/access.2021.3077888 fatcat:dw6qm3xb65fsrpgqrh4uomoipi

HAGAR: Efficient Multi-context Graph Processors [chapter]

Oskar Mencer, Zhining Huang, Lorenz Huelsbergen
2002 Lecture Notes in Computer Science  
We describe HAGAR implementations for graph reachability and shortest path.  ...  Graph algorithms, such as vertex reachability, transitive closure, and shortest path, are fundamental in many computing applications.  ...  For graphs (which we consider in this paper), the operations insert or delete graph vertices or edges. We present accompanying graph algorithms for shortest unit 1 path and reachability.  ... 
doi:10.1007/3-540-46117-5_94 fatcat:we4zyirr6bat5mn3gubqfvmeja

Diametral Reachable Index (DRI) of a Vertex

H. B.Walikar, Shreedevi V. Shindhe
2012 International Journal of Computer Applications  
Every graph has one or more diametral paths. A diametral path of a graph is a shortest path whose length is equal to the diameter of the graph. Let be a diametral vertex.  ...  For any vertex , the , if there are no diametral paths reachable from , else we write , where is the total number of diametral paths reachable from vertex .  ...  Distance in graphs: The distance between two (not necessary distinct) vertices and in a graph is the length of a shortest path between them.  ... 
doi:10.5120/7715-1174 fatcat:zs5d43ebo5ab5okrnqmuw7b6bi

Evaluating regular path queries under the all-shortest paths semantics [article]

Domagoj Vrgoč
2022 arXiv   pre-print
We then apply this algorithm to solve a similar problem in edge labelled graphs, where paths also have an additional restriction that their edge labels form a word belonging to a regular language.  ...  The purpose of this report is to explain how the textbook breadth-first search algorithm (BFS) can be modified in order to also create a compact representation of all shortest paths connecting a single  ...  We start by explaining how to obtain all shortest paths in an (unlabelled) graph, reachable from some fixed node.  ... 
arXiv:2204.11137v1 fatcat:wzfeo7fuk5gk5ludu6vvlao5ku

Computing the Fréchet distance between simple polygons in polynomial time

Kevin Buchin, Maike Buchin, Carola Wenk
2006 Proceedings of the twenty-second annual symposium on Computational geometry - SCG '06  
in the other polygon.  ...  For this, we show that it suffices to consider homeomorphisms that map an arbitrary triangulation of one polygon to the other polygon such that diagonals of the triangulation are mapped to shortest paths  ...  A feasible path starting in block B1 consists of an edge in the reachability graph of B1 from its lower to its right boundary, an edge in the combined reachability graph between the left boundary of B2  ... 
doi:10.1145/1137856.1137870 dblp:conf/compgeom/BuchinBW06 fatcat:i5trqif7u5g6neqk446z5headq

A Logspace Approximation Scheme for the Shortest Path Problem for Graphs with Bounded Independence Number [chapter]

Till Tantau
2004 Lecture Notes in Computer Science  
In contrast, for directed graphs, undirected graphs, and dags we cannot construct paths in logarithmic space (let alone approximate the shortest one), unless complexity class collapses occur.  ...  In contrast, the corresponding reachability problems for many other types of finite graphs, including dags and trees, are not first-order definable.  ...  The distance problem is closely linked to the problem of constructing the shortest path in a graph: As argued in the introduction, we can construct the shortest path in graph if we have oracle access to  ... 
doi:10.1007/978-3-540-24749-4_29 fatcat:zmzrqxwndjfo7il4zyp4ivwrc4

Generalization of the Reachability Problem on Directed Graphs

Vladimir A. Skorokhodov
2020 Mathematics and Statistics  
This approach consists in constructing an auxiliary graph and reducing the shortest path problem on a graph with non-standard reachability to a similar problem on an auxiliary graph.  ...  General approach to solving the shortest path problem on a graph with non-standard achievability is developed.  ...  Example 1 shows that classical methods for solving the shortest path problem are not applicable for graphs with reachability constraints.  ... 
doi:10.13189/ms.2020.080610 fatcat:w2gyubymhvazhbfj5mzqb2c4sm

Improved decremental algorithms for maintaining transitive closure and all-pairs shortest paths

Surender Baswana, Ramesh Hariharan, Sandeep Sen
2002 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC '02  
We present improved algorithms for maintaining transitive closure and all-pairs shortest paths/distances in a digraph under deletion of edges.  ...  form, "Is there a path from u to v in the graph?"  ...  It can be observed that for maintaining reachability (shortest paths) from u to v, it would suffice if at every stage at least one vertex on a path (the shortest path) from u to v is present in the witness  ... 
doi:10.1145/509907.509928 dblp:conf/stoc/BaswanaHS02 fatcat:mbco6e3du5hr5b5mzndsqghg2i

Improved decremental algorithms for maintaining transitive closure and all-pairs shortest paths

Surender Baswana, Ramesh Hariharan, Sandeep Sen
2002 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC '02  
We present improved algorithms for maintaining transitive closure and all-pairs shortest paths/distances in a digraph under deletion of edges.  ...  form, "Is there a path from u to v in the graph?"  ...  It can be observed that for maintaining reachability (shortest paths) from u to v, it would suffice if at every stage at least one vertex on a path (the shortest path) from u to v is present in the witness  ... 
doi:10.1145/509927.509928 fatcat:cssjmx2hpzhixgcaxe4q4c5dom

Improved decremental algorithms for maintaining transitive closure and all-pairs shortest paths

Surender Baswana, Ramesh Hariharan, Sandeep Sen
2007 Journal of Algorithms  
We present improved algorithms for maintaining transitive closure and all-pairs shortest paths/distances in a digraph under deletion of edges.  ...  form, "Is there a path from u to v in the graph?"  ...  It can be observed that for maintaining reachability (shortest paths) from u to v, it would suffice if at every stage at least one vertex on a path (the shortest path) from u to v is present in the witness  ... 
doi:10.1016/j.jalgor.2004.08.004 fatcat:mo2wrkbxija5tos7vwjqo6dehu

Extending SQL for Computing Shortest Paths

Dean De Leo, Peter Boncz
2017 Proceedings of the Fifth International Workshop on Graph Data-management Experiences & Systems - GRADES'17  
Reachability and shortest paths are among two of the most common queries realized on graphs.  ...  In this paper, we present an extension to the standard SQL language to compute both reachability predicates and many-to-many shortest path queries.  ...  Reachability and shortest path queries can be cumbersome to perform in relational databases using standard SQL. First of all, it might not be clear how to express a graph or a path in SQL.  ... 
doi:10.1145/3078447.3078457 dblp:conf/grades/LeoB17 fatcat:vvmdcvkse5b3tfs22rv2wzacym

Reachability and Distance Queries via 2-Hop Labels

Edith Cohen, Eran Halperin, Haim Kaplan, Uri Zwick
2003 SIAM journal on computing (Print)  
Reachability and distance queries in graphs are fundamental to numerous applications, ranging from geographic navigation systems to Internet routing.  ...  Some of these applications involve huge graphs and yet require fast query answering. We propose a new data structure for representing all distances in a graph.  ...  path(u, v): Find a (shortest) path from u to v in the graph.  ... 
doi:10.1137/s0097539702403098 fatcat:fuogflbvuvbgjdgkghc7h7bf2u

Computing the Fréchet distance between simple polygons

Kevin Buchin, Maike Buchin, Carola Wenk
2008 Computational geometry  
paths in a simple polygon, and dynamic programming.  ...  ., the area enclosed by closed simple polygonal curves, which may lie in different planes.  ...  Combined reachability graph The combined reachability graph combines the reachability information in the free space with valid diagonal placements and thus allows us to search for feasible paths.  ... 
doi:10.1016/j.comgeo.2007.08.003 fatcat:ngcy7avqsbehdfkxa3jy27iwgu
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