On globally solving the maximum weighted clique problem
نویسنده
چکیده
In this paper, we consider a combinatorial optimization problem, the Maximum Weighted Clique Problem (MWCP), a NP-hard problem. The considered problem is first formulated in the form of binary constrained quadratic program and then reformulated as a Difference Convex (DC) program. A global optimal solution is found by applying DC Algorithm (DCA) in combining with Branch and Bound scheme with SDP relaxation technique. Computational experiments are reported for problem instances provided by Macambria and de Souza [4] and other instances generated following the scheme of H.Späth [24].
منابع مشابه
Using modular decomposition technique to solve the maximum clique problem
In this article we use the modular decomposition technique for exact solving the weighted maximum clique problem. Our algorithm takes the modular decomposition tree from the paper of Tedder et. al. and finds solution recursively. Also, we propose algorithms to construct graphs with modules. We show some interesting results, comparing our solution with Ostergards algorithm on DIMACS benchmarks a...
متن کاملSolving the maximum edge weight clique problem via unconstrained quadratic programming
The unconstrained quadratic binary program (UQP) is proving to be a successful modeling and solution framework for a variety of combinatorial optimization problems. Experience reported in the literature with several problem classes has demonstrated that this approach works surprisingly well in terms of solution quality and computational times, often rivaling and sometimes surpassing more tradit...
متن کاملSolving the winner determination problem via a weighted maximum clique heuristic
Combinatorial auctions (CAs) where bidders can bid on combinations of items is an important model in many application areas. CAs attract more and more attention in recent years due to its relevance to fast growing electronic business applications. In this paper, we study the winner determination problem (WDP) in CAs which is known to be NP-hard and thus computationally difficult in the general ...
متن کاملOn the inverse maximum perfect matching problem under the bottleneck-type Hamming distance
Given an undirected network G(V,A,c) and a perfect matching M of G, the inverse maximum perfect matching problem consists of modifying minimally the elements of c so that M becomes a maximum perfect matching with respect to the modified vector. In this article, we consider the inverse problem when the modifications are measured by the weighted bottleneck-type Hamming distance. We propose an alg...
متن کاملA new family of facet defining inequalities for the maximum edge-weighted clique problem
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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014