673 research outputs found
Proximity Search for Maximal Subgraph Enumeration
International audienc
Efficient enumeration of maximal split subgraphs and sub-cographs and related classes
In this paper, we are interested in algorithms that take in input an
arbitrary graph , and that enumerate in output all the (inclusion-wise)
maximal "subgraphs" of which fulfil a given property . All over this
paper, we study several different properties , and the notion of subgraph
under consideration (induced or not) will vary from a result to another.
More precisely, we present efficient algorithms to list all maximal split
subgraphs, sub-cographs and some subclasses of cographs of a given input graph.
All the algorithms presented here run in polynomial delay, and moreover for
split graphs it only requires polynomial space. In order to develop an
algorithm for maximal split (edge-)subgraphs, we establish a bijection between
the maximal split subgraphs and the maximal independent sets of an auxiliary
graph. For cographs and some subclasses , the algorithms rely on a framework
recently introduced by Conte & Uno called Proximity Search. Finally we consider
the extension problem, which consists in deciding if there exists a maximal
induced subgraph satisfying a property that contains a set of prescribed
vertices and that avoids another set of vertices. We show that this problem is
NP-complete for every "interesting" hereditary property . We extend the
hardness result to some specific edge version of the extension problem
Parallel Maximum Clique Algorithms with Applications to Network Analysis and Storage
We propose a fast, parallel maximum clique algorithm for large sparse graphs
that is designed to exploit characteristics of social and information networks.
The method exhibits a roughly linear runtime scaling over real-world networks
ranging from 1000 to 100 million nodes. In a test on a social network with 1.8
billion edges, the algorithm finds the largest clique in about 20 minutes. Our
method employs a branch and bound strategy with novel and aggressive pruning
techniques. For instance, we use the core number of a vertex in combination
with a good heuristic clique finder to efficiently remove the vast majority of
the search space. In addition, we parallelize the exploration of the search
tree. During the search, processes immediately communicate changes to upper and
lower bounds on the size of maximum clique, which occasionally results in a
super-linear speedup because vertices with large search spaces can be pruned by
other processes. We apply the algorithm to two problems: to compute temporal
strong components and to compress graphs.Comment: 11 page
A Necessary and Sufficient Condition for Graph Matching to be equivalent to Clique Search
This paper formulates a necessary and sufficient condition for a generic graph matching problem to be equivalent to the maximum vertex and edge weight clique problem in a derived association graph. The consequences of this results are threefold: first, the condition is general enough to cover a broad range of practical graph matching problems; second, a proof to establish equivalence between graph matching and clique search reduces to showing that a given graph matching problem satisfies the proposed condition;\ud
and third, the result sets the scene for generic continuous solutions for a broad range of graph matching problems. To illustrate the mathematical framework, we apply it to a number of graph matching problems, including the problem of determining the graph edit distance
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