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Lower and upper bounds of shortest paths in reachability graphs

2004
*
International Journal of Mathematics and Mathematical Sciences
*

If the Petri net is a marked

doi:10.1155/s0161171204403378
fatcat:5xpbytcswnaehj3gracgpcwvs4
*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 ...##
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Subgoal Graphs for Fast Optimal Pathfinding
[chapter]

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. ...

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

2021
*
IEEE Access
*

INDEX TERMS

doi:10.1109/access.2021.3077888
fatcat:dw6qm3xb65fsrpgqrh4uomoipi
*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*. ...##
###
HAGAR: Efficient Multi-context Graph Processors
[chapter]

2002
*
Lecture Notes in Computer Science
*

We describe HAGAR implementations for

doi:10.1007/3-540-46117-5_94
fatcat:we4zyirr6bat5mn3gubqfvmeja
*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*. ...##
###
Diametral Reachable Index (DRI) of a Vertex

2012
*
International Journal of Computer Applications
*

Every

doi:10.5120/7715-1174
fatcat:zs5d43ebo5ab5okrnqmuw7b6bi
*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. ...##
###
Evaluating regular path queries under the all-shortest paths semantics
[article]

2022
*
arXiv
*
pre-print

We then apply this algorithm to solve a similar problem

arXiv:2204.11137v1
fatcat:wzfeo7fuk5gk5ludu6vvlao5ku
*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. ...##
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Computing the Fréchet distance between simple polygons in polynomial time

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 ...

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

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 ...

##
###
Generalization of the Reachability Problem on Directed Graphs

2020
*
Mathematics and Statistics
*

This approach consists

doi:10.13189/ms.2020.080610
fatcat:w2gyubymhvazhbfj5mzqb2c4sm
*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. ...##
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Improved decremental algorithms for maintaining transitive closure and all-pairs shortest paths

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

doi:10.1145/509907.509928
dblp:conf/stoc/BaswanaHS02
fatcat:mbco6e3du5hr5b5mzndsqghg2i
*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 ...##
###
Improved decremental algorithms for maintaining transitive closure and all-pairs shortest paths

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

doi:10.1145/509927.509928
fatcat:cssjmx2hpzhixgcaxe4q4c5dom
*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 ...##
###
Improved decremental algorithms for maintaining transitive closure and all-pairs shortest paths

2007
*
Journal of Algorithms
*

We present improved algorithms for maintaining transitive closure and all-pairs

doi:10.1016/j.jalgor.2004.08.004
fatcat:mo2wrkbxija5tos7vwjqo6dehu
*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 ...##
###
Extending SQL for Computing Shortest Paths

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. ...

##
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Reachability and Distance Queries via 2-Hop Labels

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*. ...

##
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Computing the Fréchet distance between simple polygons

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*. ...

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