Bomze, I.M., Budinich, M., Pardalos, P.M., Pelillo, M.: The maximum clique problem. In: D.Z. Du, P.M. Pardalos (eds.) Handbook of Combinatorial Optimization, pp. 1--74. Kluwer Academic Publishers, Dordrecht, The Netherlands (1999) Home/Search Document Details and Download
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A Hybrid Constraint Programming and Semidefinite Programming.. - van Hoeve (2003) (Correct)
....other techniques have been proposed, including approximation algorithms, heuristics, or branch and bound structured methods. A survey of di#erent formulations, complete methods and heuristics for the maximum clique problem is given by Pardalos and Xue [23] and, more recently, by Bomze et al. [4]. Although semidefinite programs can be solved in polynomial time theoretically, it lasted until a few years ago until fast solvers for this purpose were implemented. Until then, application inside a branch and bound framework was unrealistic. Still, solving a semidefinite program takes ....
I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo. The Maximum Clique Problem. In D.-Z. Du and P.M. Pardalos, editors, Handbook of Combinatorial Optimization, volume 4. Kluwer Academic Publishers, Boston, MA, 1999.
Searching for Maximum Cliques with Ant Colony Optimization - Fenet, Solnon (Correct)
....strictly included in another clique; otherwise it is maximal. The goal of the maximum clique problem is to nd a clique of maximum cardinality. This problem is one of the rst problems shown to be NP complete, and moreover, it does not admit a polynomial time approximation algorithm (unless P=NP) [2]. Hence, complete approaches usually based on a branch and bound tree search become intractable when the number of vertices increases, and much e ort has recently been directed on heuristic incomplete approaches. These approaches leave out exhaustivity and use heuristics to guide the search ....
I. Bomze, M. Budinich, P. Pardalos, and M. Pelillo. The maximum clique problem. In D.-Z. Du and P. M. Pardalos, editors, Handbook of Combinatorial Optimization, volume 4. Kluwer Academic Publishers, Boston, MA, 1999.
Trading Completeness for Scalability: Hybrid Search for Cliques.. - Prestwich (2001) (Correct)
....improves the scalability of a powerful backtracking algorithm on a hard optimisation problem. 4 Application to maximum cliques The Maximum Clique Problem (MCP) was one of the rst problems shown to be NP complete. A recent survey of its applications, algorithms and complexity results is given in [6]. The applications include computer vision, coding theory, tiling, fault diagnosis and the analysis of biological and archaeological data, and it provides a lower bound for the chromatic number of a graph. It was one of the three problems proposed in a DIMACS workshop [22] as a way of comparing ....
I. M. Bomze, M. Budinich, P. M. Pardalos, M. Pelillo. The Maximum Clique Problem. In D.-Z. Du, P. M. Pardalos (eds.), Handbook of Combinatorial Optimization volume 4, Kluwer Academic Publishers, Boston, MA, 1999. 10
Competitive Winner-Takes-All Clustering in the Domain of Graphs - Jain, Wysotzki (Correct)
....4.3 follows that the maximum of implies the maximum of (C) Thus C is a maximum M clique with (C ) This proves that is surjective. A neural maximum M clique solver Many different neural network approaches and techniques have been proposed to solve the maximum clique problem [2]. We customize the Hopfield Clique (HC) network of [25] to solve the more general maximum M clique problem. The HC network is extremely fast and outperforms greedy heuristics with respect to both speed and solution quality. The efficacy of the HC algorithm is based on a fast annealing schedule and ....
I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo. The maximum clique problem. In D.-Z. Du and P.M. Pardalos, editors, Handbook of Combinatorial Optimization, volume 4, pages 1--74. Kluwer Academic Publishers, Boston, MA, 1999.
Combining the Scalability of Local Search with the Pruning.. - Prestwich (2002) (2 citations) (Correct)
....and graph colouring. Many algorithms have been applied to the MCP on a common benchmark set, and its history, applicability and rich set of available results make the MCP ideal for evaluating new approaches. A recent survey of its applications, algorithms and complexity results is given in [7]. The MCP is defined as follows. A graph G (V , E) consists of a set V of vertices and a set E of edges between vertices. Two vertices connected by an edge are said to be adjacent.Aclique is a subset of V whose vertices are pairwise adjacent. A maximum clique is a clique of maximum ....
I.M. Bomze, M. Budinich, P.M. Pardalos and M. Pelillo, The Maximum Clique Problem, in: Handbook of Combinatorial Optimization, Vol. 4, eds. D.-Z. Du and P.M. Pardalos (Kluwer Academic, Boston, MA, 1999).
A Heuristic for the Maximum Independent Set Problem Based.. - Busygin, Butenko, al. (2002) Self-citation (Pardalos) (Correct)
No context found.
I. M. Bomze, M. Budinich, P. M. Pardalos, and M. Pelillo. The maximum clique problem. In D.-Z. Du and P. M. Pardalos, editors, Handbook of Combinatorial Optimization, pages 1--74. Kluwer Acad. Publishers, 1999.
Mining market data: A network approach - Boginski, Butenko, Pardalos (2005) Self-citation (Pardalos) (Correct)
No context found.
Bomze IM, Budinich M, Pardalos PM, Pelillo M. The maximum clique problem. In: Du D-Z, Pardalos PM, editors. Handbook of combinatorial optimization. Dordrecht: Kluwer Academic Publishers; 1999. p. 1--74.
Annealed Imitation: Fast Dynamics for Maximum Clique - Marcello Pelillo Dipartimento Self-citation (Pelillo) (Correct)
....directed towards devising efficient clique finding heuristics, for which no formal guarantee of performance may be provided, but are anyway of interest in practical applications. In the neural network community, there has also been much recent interest around this important problem. We refer to [2] for a recent review concerning algorithms, applications, and complexity issues related to the MCP. In the mid 1960s, Motzkin and Straus [11] established a remarkable connection between the MCP and a quadratic programming problem on the standard simplex. The MotzkinStraus formulation, and ....
I. M. Bomze, M. Budinich, P. M. Pardalos, and M. Pelillo, "The maximum clique problem," In Handbook of Combinatorial Optimization (Suppl. Vol. A), D.-Z. Du and P. M. Pardalos, Eds. Boston, MA: Kluwer, 1999, pp. 1--74.
Matching Free Trees, Maximal Cliques, and Monotone Game Dynamics - Pelillo (2002) Self-citation (Pelillo) (Correct)
....theory and powerful algorithms have been developed. Note that, although the maximum clique problem is known to be NP hard, powerful heuristics exist which efficiently find good approximate solutions and there exist several classes of graphs for which the problem can be solved in polynomial time [5]. In many computer vision problems, the graphs at hand have a peculiar structure: they are connected and acyclic, i.e. they are free trees (see, e.g. 3] 16] 18] 26] Other application domains where free trees arise quite frequently are pattern recognition [9] and biochemistry [1] Note ....
....[2] A subset of vertices of a graph G is said to be a clique if all its nodes are mutually adjacent. A maximal clique is one which is not contained in any larger clique, while a maximum clique is a clique having the largest cardinality. The maximum clique problem is to find a maximum clique of G [5]. The main result of this section establishes a one to one correspondence between maximal maximum subtree isomorphisms and maximal maximum cliques in the FTAG. To prove it, we first need the following lemma. Lemma 1. Let u 1 ;v 1 ;w 1 ;z 1 V 1 and u 2 ;v 2 ;w 2 ;z 2 V 2 be distinct nodes of ....
I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo, "The Maximum Clique Problem," Handbook of Combinatorial Optimization (supplement vol. A), D.-Z. Du and P.M. Pardalos, eds., pp. 1-74, Boston: Kluwer, 1999.
Finding Independent Sets In A Graph Using.. - Abello, Butenko.. (2001) (3 citations) Self-citation (Pardalos) (Correct)
....graph G is equal to the minimum cardinality of a vertex cover. Practical applications of these optimization problems are abundant. They appear in information retrieval, signal transmission analysis, classification theory, economics, scheduling, experimental design, and computer vision. See [1, 2, 5, 3, 4, 9, 22, 26] for details. The remainder of this paper is organized as follows. In Section 2 we review some integer programming and continuous formulations of the maximum independent set problem. Two new polynomial formulations are proposed in Section 3. In Section 4, we show how the Motzkin Straus theorem ....
I. M. Bomze, M. Budinich, P. M. Pardalos, and M. Pelillo. The maximum clique problem. In D.-Z. Du and P. M. Pardalos, editors, Handbook of Combinatorial Optimization, pages 1--74. Kluwer Acad. Publishers, 1999.
B. Balasundaram - Butenko Hicks Sachdeva (Correct)
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Bomze, I.M., Budinich, M., Pardalos, P.M., Pelillo, M.: The maximum clique problem. In: D.Z. Du, P.M. Pardalos (eds.) Handbook of Combinatorial Optimization, pp. 1--74. Kluwer Academic Publishers, Dordrecht, The Netherlands (1999)
Exploiting Semidefinite Relaxations in Constraint Programming - van Hoeve (2003) (Correct)
No context found.
I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo. The Maximum Clique Problem. In D.-Z. Du and P.M. Pardalos, editors, Handbook of Combinatorial Optimization, volume 4. Kluwer, 1999.
A Hybrid Constraint Programming and Semidefinite Programming.. - van Hoeve (2003) (Correct)
No context found.
I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo. The Maximum Clique Problem. In D.-Z. Du and P.M. Pardalos, editors, Handbook of Combinatorial Optimization, volume 4. Kluwer Academic Publishers, Boston, MA, 1999.
Reformulation and Convex Relaxation Techniques for Global.. - Liberti (2004) (Correct)
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I. Bomze, M. Budinich, P. Pardalos, and M. Pelillo. The maximum clique problem. In Du and Pardalos [28], pages 1--74.
Using Critical Sets for the Maximum Independent Set Problem.. - Butenko, Trukhanov (Correct)
No context found.
I. M. Bomze, M. Budinich, P. M. Pardalos, and M. Pelillo. The maximum clique problem. In D.-Z. Du and P. M. Pardalos, editors, Handbook of Combinatorial Optimization, pages 1--74. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.
Clique-detection Models in Computational Biochemistry and.. - Butenko, Wilhelm (2005) (Correct)
No context found.
Bomze, I. M., Budinich, M., Pardalos, P. M., Pelillo, M., 1999. The maximum clique problem. In: Du, D.-Z., Pardalos, P. M. (Eds.), Handbook of Combinatorial Optimization. Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 1--74.
Constructing Test Functions for Global Optimization Using.. - Balasundaram, Butenko (2005) (Correct)
No context found.
Bomze, I. M., Budinich, M., Pardalos, P. M. and Pelillo, M., 1999, The maximum clique problem. In: D.-Z. Du and P. M. Pardalos (Eds) Handbook of Combinatorial Optimization (Dordrecht, The Netherlands: Kluwer Academic), pp. 1--74.
Novel Approaches for Analyzing Biological Networks - Balasundaram, Butenko.. (2005) (Correct)
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I. M. Bomze, M. Budinich, P. M. Pardalos, and M. Pelillo. The maximum clique problem. In D.-Z. Du and P. M. Pardalos, editors, Handbook of Combinatorial Optimization, pages 1--74. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.
A Hybrid Constraint Programming and Semidefinite Programming.. - van Hoeve (2003) (Correct)
No context found.
I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo. The Maximum Clique Problem. In D.-Z. Du and P.M. Pardalos, editors, Handbook of Combinatorial Optimization, volume 4. Kluwer Academic Publishers, Boston, MA, 1999.
Exploiting Semidefinite Relaxations in Constraint Programming - van Hoeve (Correct)
No context found.
I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo. The Maximum Clique Problem. In D.-Z. Du and P.M. Pardalos, editors, Handbook of Combinatorial Optimization, volume 4. Kluwer, 1999.
Computational, Integrative and Comparative Methods .. - Baldwin, Chesler, .. (Correct)
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I. Bomze, M. Budinich, P. Pardalos, and M. Pelillo. The maximum clique problem. In D.-Z. Du and P. M. Pardalos, editors, Handbook of Combinatorial Optimization, volume 4. Kluwer Academic Publishers, 1999.
Mobile Robot Localisation and Mapping in Extensive Outdoor.. - Bailey (2002) (10 citations) (Correct)
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I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo. The maximum clique problem. In D.Z. Du and P.M. Pardalos, editors, Handbook of Combinatorial Optimization. Kluwer Academic Publishers, 1999.
Induction of Semantic Classes from Natural Language Text - Dekang Lin And (2001) (2 citations) (Correct)
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Bomze, I. M., Budinich, M., Pardalos, P. M., and Pelillo, M. 1999. The maximum clique problem. Handbook of Combinatorial Optimization (Supplement Volume A). D.-Z. Du and P. M. Pardalos (Eds.). Kluwer Academic Publishers. Boston, MA. pp. 1-74
Properties Of Nonuniform Random Graph Models - Virtanen (2003) (1 citation) (Correct)
No context found.
I. M. Bomze, M. Budinich, P. M. Pardalos, and M. Pelillo. The maximum clique problem. In D.-Z. Du and P. M. Pardalos, editors, Handbook of Combinatorial Optimization, volume Suppl. A, pages 1--74. Kluwer Academic Publishers, Boston, MA, USA, 1999.
Investigating ACO capabilities for solving the Maximum Clique.. - Solnon, Fenet (2004) (Correct)
No context found.
I. Bomze, M. Budinich, P. Pardalos, and M. Pelillo. The maximum clique problem. In D.-Z. Du and P. M. Pardalos, editors, Handbook of Combinatorial Optimization, volume 4. Kluwer Academic Publishers, Boston, MA, 1999.
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