Enumeration of all simple paths in a directed graph using Petri net: A systematic approach

Hura, Gurdeep S.

doi:10.1016/0026-2714(83)91381-1

Cited by 10 publications

(5 citation statements)

References 3 publications

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“…It is not clear whether it is an NP‐hard problem or is polynomial‐time solvable. We conjecture that it is polynomially solvable, because in the algorithms developed in this study MFR searching involves little additional complexity compared to finding all simple paths between two given nodes, and the latter has polynomial‐time algorithms (Rubin, ; Khan and Singh, ; Misra and Misra, ; Hura, ). However, hypergraph problems can be more complex than general graph problems.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Path‐based routing studies in graph theory provide theoretical foundations and methodologies for practical applications. Many algorithms have been developed to solve different path problems in a graph, e.g., to find all simple paths between any pair or a given pair of nodes (Rubin, ; Misra and Misra, ; Hura, ), detect the shortest path or k shortest paths between two nodes (Dijkstra, ; Floyd, ; Eppstein, ; Roditty, ), or to find the longest path between two nodes (Karger et al, ; Scutellà, ). In classic graph models, edges ending at a node are assumed to be independent.…”

Section: Introductionmentioning

confidence: 99%

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Minimal functional routes in directed graphs with dependent edges

Wang

Sun

Albert

2013

Int Trans Operational Res

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Graphs are mathematical structures used to model a set of objects and the relations between them. One of the basic concepts of graph theory, the path, has wide real-world applications. In classic graph models, edges ending at a node are assumed to be independent. However, many real graphs/networks can only be correctly described by considering a dependency among nodes or edges. Paths in such graphs may not be functional if the conditional dependency is ignored. In this study, we investigate the routing problem in directed graphs with dependent edges represented by general graph models as alternatives to hypergraphs. We define a minimal functional route (MFR) as a minimal set of nodes and edges that can independently perform information transfer between two given nodes, and formulate the determination of MFRs as a graph search problem. A depth-first-search (DFS) top-down algorithm, an iterative integer linear programming (ILP) bottom-up algorithm, and a subgraph-growing bottom-up algorithm are devised subsequently to solve this problem. Numerical experiments verify the effectiveness of the algorithms. The defined MFR problem and the proposed algorithms are expected to find many practical applications.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Minimal functional routes in directed graphs with dependent edges

Wang

Sun

Albert

2013

Int Trans Operational Res

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“…In one of the earlier studies, Valiant [25] showed that it is #P-complete to enumerate simple s − t paths in both directed and undirected graphs. In [10], Hura utilized Petri nets to enumerate all s − t simple paths in a directed graph. Bax [2] Knuth [11] presented the simpath algorithm that generates a (not-always-reduced) binary decision diagram for all simple paths from s to t. The constructed diagram is called zero-suppressed decision diagram (ZDD).…”

Section: Related Workmentioning

confidence: 99%

Effectively Counting s-t Simple Paths in Directed Graphs

Chehreghani¹

2021

Preprint

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An important tool in analyzing complex social and information networks is s−t simple path counting, which is known to be #P-complete. In this paper, we study efficient s − t simple path counting in directed graphs. For a given pair of vertices s and t in a directed graph, first we propose a pruning technique that can efficiently and considerably reduce the search space. Then, we discuss how this technique can be adjusted with exact and approximate algorithms, to improve their efficiency. In the end, by performing extensive experiments over several networks from different domains, we show high empirical efficiency of our proposed technique. Our algorithm is not a competitor of existing methods, rather, it is a friend that can be used as a fast pre-processing step, before applying any existing algorithm.

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“…Alternatively, the simple paths can also be enumerated using another property o f Petri nets, i.e., Conflict [73]. The conflict occurs when a place makes more than one transitions fireable simultaneously i.e., these transitions are having this place as an input place.…”

Section: (I) Find a And δ M As Discussed Above (Ii) From A Find All mentioning

confidence: 99%

“…The following two properties are defined for the proposed technique and the proof and other details can be found in [73].…”

Section: The Ce O F Ps At the (N-2) 1 Level Will Yield All The Simplementioning

confidence: 99%

Use of Petri Nets for System Reliability Evaluation

Hura

1993

Fundamental Studies in Engineering

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Enumeration of all simple paths in a directed graph using Petri net: A systematic approach

Cited by 10 publications

References 3 publications

Minimal functional routes in directed graphs with dependent edges

Minimal functional routes in directed graphs with dependent edges

Effectively Counting s-t Simple Paths in Directed Graphs

Use of Petri Nets for System Reliability Evaluation

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