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Lecture Notes in Computer Science
We introduce the graph parameter boolean-width, related to the number of different unions of neighborhoods -Boolean sums of neighborhoods -across a cut of a graph. For many graph problems, this number is the runtime bottleneck when using a divide-andconquer approach. For an n-vertex graph given with a decomposition tree of boolean-width k, we solve Maximum Weight Independent Set in time O(n 2 k2 2k ) and Minimum Weight Dominating Set in time O(n 2 + nk2 3k ). With an additional n 2 factor indoi:10.1007/978-3-642-11269-0_5 fatcat:xer24xhbnbh3bdqauzggqfw2b4