منابع مشابه
Set Partitioning via Inclusion-Exclusion
Given a set N with n elements and a family F of subsets, we show how to partition N into k such subsets in 2nnO(1) time. We also consider variations of this problem where the subsets may overlap or are weighted, and we solve the decision, counting, summation, and optimisation versions of these problems. Our algorithms are based on the principle of inclusion–exclusion and the zeta transform. In ...
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Set multi-covering is a generalization of the set covering problem where each element may need to be covered more than once and thus some subset in the given family of subsets may be picked several times for minimizing the number of sets to satisfy the coverage requirement. In this paper, we propose a family of exact algorithms for the set multi-covering problem based on the inclusionexclusion ...
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Inclusion/exclusion branching is a way to branch on requirements imposed on problems, in contrast to the classical branching on parts of the solution. The technique turned out to be useful for finding and counting (minimum) dominating sets (van Rooij et al., ESA 2009). In this paper, we extend the technique to the setting where one is given a set of properties and seeks (or wants to count) solu...
متن کاملImproved inclusion-exclusion identities via closure operators
Improved inclusion-exclusion identities via closure operators Klaus Dohmen Department of Computer Science, Humboldt-University Berlin, Unter den Linden 6, D-10099 Berlin, Germany E-mail: [email protected] received March 24, 1999, revised September 6, 1999, accepted April 15, 2000. Let be a finite family of sets. We establish an improved inclusion-exclusion identity for each closure...
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When evaluating the inclusion-exclusion expansion N0 −N(1) −N(2) − · · ·+N(1, 2) +N(1, 3) + · · · many of the terms N(· · ·) may turn out to be zero, and hence should be discarded beforehand. Often this can be done.
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2009
ISSN: 0097-5397,1095-7111
DOI: 10.1137/070683933