Efficient Enumeration of Bipartite Subgraphs in Graphs

Wasa, Kiyotaka; Uno, Takeaki

doi:10.1007/978-3-319-94776-1_38

Cited by 5 publications

(5 citation statements)

References 24 publications

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“…Maximal bipartite subgraphs have also been studied as minimal odd cycle transversals [19], as one is the complement of the other. The problem of listing all bipartite (and induced bipartite) subgraphs has been efficiently solved in [34]. However, to the best of our knowledge, neither the techniques in [34] or other known ones extend to efficiently listing maximal bipartite subgraphs.…”

Section: Maximal Bipartite Subgraphsmentioning

confidence: 99%

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New polynomial delay bounds for maximal subgraph enumeration by proximity search

Conte

Uno

2019

Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

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In this paper we propose polynomial delay algorithms for several maximal subgraph listing problems, by means of a seemingly novel technique which we call proximity search. Our result involves modeling the space of solutions as an implicit directed graph called "solution graph", a method common to other enumeration paradigms such as reverse search. Such methods, however, can become inefficient due to this graph having vertices with high (potentially exponential) degree. The novelty of our algorithm consists in providing a technique for generating better solution graphs, reducing the out-degree of its vertices with respect to existing approaches, and proving that it remains strongly connected. Applying this technique, we obtain polynomial delay listing algorithms for several problems for which output-sensitive results were, to the best of our knowledge, not known. These include Maximal Bipartite Subgraphs, Maximal k-Degenerate Subgraphs (for bounded k), Maximal Induced Chordal Subgraphs, and Maximal Induced Trees. We present these algorithms, and give insight on how this general technique can be applied to other problems.

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Section: Maximal Bipartite Subgraphsmentioning

confidence: 99%

“…The problem of listing all bipartite (and induced bipartite) subgraphs has been efficiently solved in [34]. However, to the best of our knowledge, neither the techniques in [34] or other known ones extend to efficiently listing maximal bipartite subgraphs.…”

Section: Maximal Bipartite Subgraphsmentioning

confidence: 99%

New polynomial delay bounds for maximal subgraph enumeration by proximity search

Conte

Uno

2019

Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

Self Cite

View full text Add to dashboard Cite

show abstract

“…The problem of listing all bipartite (and induced bipartite) subgraphs has been efficiently solved in [37]. However, to the best of our knowledge, neither the techniques in [37] or other known ones extend to efficiently listing maximal bipartite subgraphs.…”

Section: Maximal Bipartite Subgraphsmentioning

confidence: 99%

Proximity Search For Maximal Subgraph Enumeration

Conte¹,

Marino²,

Grossi³

et al. 2019

Preprint

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This paper considers the subgraphs of an input graph that satisfy a given property and are maximal under inclusion. The main result is a seemingly novel technique, proximity search, to list these subgraphs in polynomial delay each. These include Maximal Bipartite Subgraphs, Maximal k-Degenerate Subgraphs (for bounded k), Maximal Induced Chordal Subgraphs, and Maximal Induced Trees. Using known techniques, such as reverse search, the space of sought solutions induces an implicit directed graph called "solution graph": however, the latter can give rise to exponential out-degree, thus preventing polynomial delay. The novelty of our algorithm in this paper consists in providing a technique for generating a better solution graph, significantly reducing the out-degree with respect to existing approaches, so that it still remains strongly connected and guarantees that all solutions can be reported with polynomial delay by a suitable traversal. While traversing the solution graph incur in space proportional to the number of solutions to keep track of visited ones, we further propose a technique to induce a parent-child relationship and achieve polynomial space when suitable conditions are met. 1 CCS CONCEPTS• Mathematics of computing → Graph enumeration; Graph algorithms.

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“…Moreover, an enumeration algorithm is amortized polynomial if the total running time is O(M • poly(N )) time, where M is the number of solutions, N is the input size, and poly is a polynomial function. In enumeration algorithm area, there are efficient algorithms for sparse graphs [6,9,12,15,19,20]. Especially, the degeneracy [16] of graphs has been payed much attention for constructing efficient enumeration algorithms.…”

Section: Intorductionmentioning

confidence: 99%

An Efficient Algorithm for Enumerating Chordal Bipartite Induced Subgraphs in Sparse Graphs

Kurita

Wasa

Uno

et al. 2019

Lecture Notes in Computer Science

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In this paper, we propose a characterization of chordal bipartite graphs and an efficient enumeration algorithm for chordal bipartite induced subgraphs. A chordal bipartite graph is a bipartite graph without induced cycles with length six or more. It is known that the incident graph of a hypergraph is chordal bipartite graph if and only if the hypergraph is β-acyclic. As the main result of our paper, we show that a graph G is chordal bipartite if and only if there is a special vertex elimination ordering for G, called CBEO. Moreover, we propose an algorithm ECB which enumerates all chordal bipartite induced subgraphs in O(kt∆ 2 ) time per solution on average, where k is the degeneracy, t is the maximum size of Kt,t as an induced subgraph, and ∆ is the degree. ECB achieves constant amortized time enumeration for bounded degree graphs.

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Efficient Enumeration of Bipartite Subgraphs in Graphs

Cited by 5 publications

References 24 publications

New polynomial delay bounds for maximal subgraph enumeration by proximity search

New polynomial delay bounds for maximal subgraph enumeration by proximity search

Proximity Search For Maximal Subgraph Enumeration

An Efficient Algorithm for Enumerating Chordal Bipartite Induced Subgraphs in Sparse Graphs

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