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arXiv · 1906.09680

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

Kazuhiro Kurita·Kunihiro Wasa·Hiroki Arimura·Takeaki Uno
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Abstract

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 $\texttt{EIS}$ 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 $\texttt{EIS}$ works correctly even if the exact value of $q$ is unknown. Despite its simplicity, $\texttt{EIS}$ 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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Kazuhiro Kurita, Kunihiro Wasa, Hiroki Arimura, Takeaki Uno. 2019-06-24. Constant Amortized Time Enumeration of Independent Sets for Graphs with Bounded Clique Number. https://doi.org/10.1016/j.tcs.2021.05.008

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