Average case complete problems
SIAM Journal on Computing
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Journal of Algorithms
Polynomial approximation algorithms for the TSP and the QAP with a factorial domination number
Discrete Applied Mathematics
Linear Time Dynamic-Programming Algorithms for New Classes of Restricted TSPs: A Computational Study
INFORMS Journal on Computing
Free bits, PCPs and non-approximability-towards tight results
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Domination analysis of combinatorial optimization problems
Discrete Applied Mathematics
Algorithms with large domination ratio
Journal of Algorithms
TSP tour domination and Hamilton cycle decompositions of regular digraphs
Operations Research Letters
Domination analysis for minimum multiprocessor scheduling
Discrete Applied Mathematics
Dominance guarantees for above-average solutions
Discrete Optimization
Domination analysis of algorithms for bipartite boolean quadratic programs
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
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The design and analysis of approximation algorithms for NP-hard problems is perhaps the most active research area in the theory of combinatorial algorithms. In this article, we study the notion of a combinatorial dominance guarantee as a way for assessing the performance of a given approximation algorithm. An f(n) dominance bound is a guarantee that the heuristic always returns a solution not worse than at least f(n) solutions. We give tight analysis of many heuristics, and establish novel and interesting dominance guarantees even for certain inapproximable problems and heuristic search algorithms. For example, we show that the maximal matching heuristic of VERTEX COVER offers a combinatorial dominance guarantee of 2n − (1.839 + o(1))n. We also give inapproximability results for most of the problems we discuss.