Satellites and Mirrors for Solving Independent Set on Sparse Graphs

In this paper, we study the well-known Maximum Independent Set (MIS)problem: Given a graph G = (V,E) with n nodes and m edges, the problemis to find an independent set I ⊆ V of maximum size α(G), i.e., a set I ⊆ Vsuch that no two nodes in I are adjacent. This problem is known to be NP-complete [11] even on graphs of a maximum degree of three (cubic graphs).Being a problem with a long research history, there are already numerous resultsregarding approximation algorithms, randomized algorithms, or otherapproachesfor MIS on sparse graphs, see, e.g., [1,3,4,9]. Here, we concentrate on exactalgorithms for sparse graphs. For exact algorithms on arbitrary graphs, we referthe reader to the latest corresponding results, which are due to Robson [13] anddue to Fomin, Grandoni, and Kratsch [7].Recently, there have been various new results for MIS on sparse graphs:In 1999, Beigel [2] introduced an O

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