Topic
Set packing
About: Set packing is a research topic. Over the lifetime, 833 publications have been published within this topic receiving 27485 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: For the problem of finding the maximum clique in a graph, no algorithm has been found for which the ratio does not grow at least as fast as n^@e, where n is the problem size and @e>0 depends on the algorithm.
2,572 citations
TL;DR: A survey of results concerning algorithms, complexity, and applications of the maximum clique problem is presented and enumerative and exact algorithms, heuristics, and a variety of other proposed methods are discussed.
Abstract: The maximum clique problem is a classical problem in combinatorial optimization which finds important applications in different domains. In this paper we try to give a survey of results concerning algorithms, complexity, and applications of this problem, and also provide an updated bibliography. Of course, we build upon precursory works with similar goals [39, 232, 266].
1,175 citations
TL;DR: This work considers problems requiring to allocate a set of rectangular items to larger rectangular standardized units by minimizing the waste by discussing mathematical models, lower bounds, classical approximation algorithms, recent heuristic and metaheuristic methods and exact enumerative approaches.
914 citations
TL;DR: An exact algorithm for filling a single bin is developed, leading to the definition of an exact branch-and-bound algorithm for the three-dimensional bin packing problem, which also incorporates original approximation algorithms.
Abstract: The problem addressed in this paper is that of orthogonally packing a given set of rectangular-shaped items into the minimum number of three-dimensional rectangular bins. The problem is strongly NP-hard and extremely difficult to solve in practice. Lower bounds are discussed, and it is proved that the asymptotic worst-case performance ratio of the continuous lower bound is ?. An exact algorithm for filling a single bin is developed, leading to the definition of an exact branch-and-bound algorithm for the three-dimensional bin packing problem, which also incorporates original approximation algorithms. Extensive computational results, involving instances with up to 90 items, are presented: It is shown that many instances can be solved to optimality within a reasonable time limit.
703 citations
TL;DR: This paper shows that the cliques of the intersection graph provide a first set of facets for the polyhedron in question, and it is shown that the cycles without chords of odd length of the intersections graph give rise to a further set of facet.
Abstract: In this paper we address ourselves to identifying facets of the set packing polyhedron, i.e., of the convex hull of integer solutions to the set covering problem with equality constraints and/or constraints of the form "ź". This is done by using the equivalent node-packing problem derived from the intersection graph associated with the problem under consideration. First, we show that the cliques of the intersection graph provide a first set of facets for the polyhedron in question. Second, it is shown that the cycles without chords of odd length of the intersection graph give rise to a further set of facets. A rather strong geometric property of this set of facets is exhibited.
665 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 2 |
| 2024 | 2 |
| 2023 | 2 |
| 2022 | 12 |
| 2021 | 9 |
| 2020 | 13 |