Solving the maximum edge weight clique problem via unconstrained quadratic programming

Alidaee, Bahram; Glover, Fred; Kochenberger, Gary A.; Wang, Haibo

doi:10.1016/j.ejor.2006.06.035

Cited by 57 publications

(31 citation statements)

References 13 publications

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“…We refer the reader to [19,7,13,11,9,8,14,3,1] for more details on other existing facet defining inequalities and solution methods for the MEWCP. For the sake of brevity, we restrict our literature review to the paper of Djeumou Fomeni et al [4] in which they presented the cutting planes that are discussed in this paper.…”

Section: Literature Reviewmentioning

confidence: 99%

A new family of facet defining inequalities for the maximum edge-weighted clique problem

Fomeni

2016

Optim Lett

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This paper considers a family of cutting planes, recently developed for mixed 0-1 polynomial programs and shows that they define facets for the maximum edge-weighted clique problem. There exists a polynomial time exact separation algorithm for these inequalities. The result of this paper may contribute to the development of more efficient algorithms for the maximum edge-weighted clique problem that use cutting planes.

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Section: Literature Reviewmentioning

confidence: 99%

A new family of facet defining inequalities for the maximum edge-weighted clique problem

Fomeni

2016

Optim Lett

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“…Indeed, scalarized Z with respect to Weighted-sum includes, as special case, the problem of finding a set of participating source nodes with the maximum spatial dispersion. The latter leads to solving MEWCP, which is a well-known NP-hard problem [3]. Now, consider MEWCP in a complete graph G c with n vertices v 1 , .…”

Section: Approximate Solutionmentioning

confidence: 99%

“…Moreover, X[i, W i ] denotes the maximum number of source successors 2 (including i only if i is a source) that i can account for aggregation. For each i, let H(i) ⊆ V be a set consisting of node i and all its predecessors 3 (except the sink) in the aggregation tree. Moreover, let K i be the set of children of node i with cardinality K i .…”

Section: A Wsn Modelmentioning

confidence: 99%

“…This leads to the extension of the framework of [2] to a bi-objective combinatorial optimization problem. We prove that solving the formulated problem, i.e., finding a Pareto-optimal solution, is at least as hard as the Maximum Edge Weighted Clique Problem (MEWCP), which is known to be NP-hard [3]. In order to find an approximate Pareto-optimal solution, we then propose SDMAX as a heuristic distributed algorithm that (1) selects source participants and (2) assigns waiting times for a delay-constrained interference-free aggregation in treebased WSNs.…”

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confidence: 99%

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Maximizing Quality of Aggregation in Delay-Constrained Wireless Sensor Networks

et al. 2013

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Abstract-In this letter, both the number of participating nodes and spatial dispersion are incorporated to establish a bi-objective optimization problem for maximizing the quality of aggregation under interference and delay constraints in tree-based wireless sensor networks (WSNs). The formulated problem is proved to be NP-hard with respect to Weighted-sum scalarization and a distributed heuristic aggregation scheduling algorithm, named SDMAX, is proposed. Simulation results show that SDMAX not only gives a close approximation of the Pareto-optimal solution, but also outperforms the best, to our knowledge, existing alternative proposed so far in the literature.

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“…It is also a useful approach for problems involved with a bi-partite graph to be formulated as an unconstrained quadratic binary programming problem [1].…”

Section: Unconstrained Quadratic Binary Programmingmentioning

confidence: 99%

Weighted Rank-One Binary Matrix Factorization

Vaidya

Atluri

et al. 2011

Proceedings of the 2011 SIAM International Conference on Data Mining

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Mining discrete patterns in binary data is important for many data analysis tasks, such as data sampling, compression, and clustering. An example is that replacing individual records with their patterns would greatly reduce data size and simplify subsequent data analysis tasks. As a straightforward approach, rank-one binary matrix approximation has been actively studied recently for mining discrete patterns from binary data. It factorizes a binary matrix into the multiplication of one binary pattern vector and one binary presence vector, while minimizing mismatching entries. However, this approach suffers from two serious problems. First, if all records are replaced with their respective patterns, the noise could make as much as 50% in the resulting approximate data. This is because the approach simply assumes that a pattern is present in a record as long as their matching entries are more than their mismatching entries. Second, two error types, 1-becoming-0 and 0-becoming-1, are treated evenly, while in many application domains they are discriminated. To address the two issues, we propose weighted rank-one binary matrix approximation. It enables the tradeoff between the accuracy and succinctness in approximate data and allows users to impose their personal preferences on the importance of different error types. The decision problem, however, as proved in the paper is NP-complete. To solve it, several different mathematical programming formulations are provided, from which 2-approximation algorithms are derived for some special cases. An adaptive tabu search heuristic is presented for solving the general problem, and our experimental study shows the effectiveness of the heuristic.

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Solving the maximum edge weight clique problem via unconstrained quadratic programming

Cited by 57 publications

References 13 publications

A new family of facet defining inequalities for the maximum edge-weighted clique problem

A new family of facet defining inequalities for the maximum edge-weighted clique problem

Maximizing Quality of Aggregation in Delay-Constrained Wireless Sensor Networks

Weighted Rank-One Binary Matrix Factorization

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