Counting and enumerating independent sets with applications to combinatorial optimization problems

被引：3
|
作者：
Gurski, Frank [1 ]
Rehs, Carolin [1 ]
机构：
[1] Univ Dusseldorf, Inst Comp Sci, Algorithm Hard Problems Grp, D-40225 Dusseldorf, Germany
来源：
MATHEMATICAL METHODS OF OPERATIONS RESEARCH | 2020年 / 91卷 / 03期
关键词：
Knapsack problem; Multidimensional knapsack problem; Threshold graphs; Independent sets; KNAPSACK-PROBLEMS; GRAPHS; ALGORITHMS; COMPLEXITY; CONFLICT;
D O I：
10.1007/s00186-019-00696-4
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
Counting and enumerating maximal and maximum independent sets are well-studied problems in graph theory. In this paper we introduce methods to count and enumerate maximal/maximum independent sets in threshold graphs andk-threshold graphs and improve former results for these problems. The results can be applied to combinatorial optimization problems, and in particular to different variations of the knapsack problem. As feasible solutions for instances of those problems correspond to independent sets in threshold graphs andk-threshold graphs, we obtain polynomial time results for special knapsack and multidimensional knapsack instances. Also, we show lower and upper bounds for the number of necessary bins in several bin packing problems.
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页码：439 / 463
页数：25
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