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Constant Amortized Time Enumeration of Independent Sets for Graphs with Bounded Clique Number

06/24/2019
by   Kazuhiro Kurita, et al.
National Institute of Informatics
Hokkaido University
0

In this study, we address the independent set enumeration problem. Although several efficient enumeration algorithms and careful analyses have been proposed for maximal independent sets, no fine-grained analysis has been given for the non-maximal variant. From the main result, we propose an algorithm EIS for the non-maximal variant that runs in O(q) amortized time and linear space, where q is the clique number, i.e., the maximum size of a clique in an input graph. Note that EIS works correctly even if the exact value of q is unknown. Despite its simplicity, EIS is optimal for graphs with a bounded clique number, such as, triangle-free graphs, planar graphs, bounded degenerate graphs, locally bounded expansion graphs, and F-free graphs for any fixed graph F, where a F-free graph is a graph that has no copy of F as a subgraph.

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