Flow Hypergraph Reducibility

Guedes, André Luiz Pires; Markenzon, Lilian; Faria, Luérbio

doi:10.1016/j.endm.2008.01.044

Cited by 1 publication

(2 citation statements)

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“…On the other side, find classes where dominators can be found in less than O(n • S(H)) time. One possible candidate class are the reducible flow hypergraphs [4]. Independently of hypernetworks, we believe that the computation of dominators in flow hypergraphs may be an interesting subject for further research.…”

Section: Discussionmentioning

confidence: 99%

“…Hypernetworks can be related to the concepts of flow hypergraph and dominator. Flow hypergraphs, introduced by Guedes et al [4], extend the well known concept of flowgraph to the broader class of hypergraphs introduced by Gallo et al [1]. We say that H = (V, E) is a flow hypergraph with source s ∈ V if each node in V is hyperconnected to s in H; this can be denoted by H = (V, E, s).…”

Section: Definitions and Main Propertiesmentioning

confidence: 99%

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Finding hypernetworks in directed hypergraphs

Pretolani

2013

European Journal of Operational Research

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The term ‘‘hypernetwork’’ (more precisely, s-hypernetwork and (s, d)-hypernetwork) has been recently adopted to denote some logical structures contained in a directed hypergraph. A hypernetwork identifies the core of a hypergraph model, obtained by filtering off redundant components. Therefore, finding hypernetworks has a notable relevance both from a theoretical and from a computational point of view.\ud In this paper we provide a simple and fast algorithm for finding s-hypernetworks, which substantially improves on a method previously proposed in the literature. We also point out two linearly solvable particular cases.\ud Finding an (s, d)-hypernetwork is known to be a hard problem, and only one polynomially solvable class has been found so far. Here we point out that this particular case is solvable in linear time

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Section: Discussionmentioning

confidence: 99%

Section: Definitions and Main Propertiesmentioning

confidence: 99%