Fuzzy Combinatorial Optimization Problems

Pardalos, Pãnos M.; Aydoğan, Emel Kızılkaya; Gürbüz, Feyza; Demirtaş, Özgür; Bakirli, Birce Boga

doi:10.1007/978-1-4419-7997-1_68

Cited by 7 publications

(3 citation statements)

References 157 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A well-known percolation problem is the emergence of the giant connected component (GCC) [9][10][11][12]. A combinatorial optimization problem on a graph [13,14] usually concerns finding an optimal set of vertices or edges under a structural constraint. The difficulty in finding solutions leads to the study of computational complexity classes [15], whose typical examples are the polynomial and the non-deterministic polynomial-time-hard (NP-hard) problems.…”

Section: Introductionmentioning

confidence: 99%

Two faces of greedy leaf removal procedure on graphs

Zhao¹,

Zhou²

2019

J. Stat. Mech.

View full text Add to dashboard Cite

The greedy leaf removal (GLR) procedure on a graph is an iterative removal of any vertex with degree one (leaf) along with its nearest neighbor (root). Its result has two faces: a residual subgraph as a core, and a set of removed roots. While the emergence of cores on uncorrelated random graphs was solved analytically, a theory for roots is ignored except in the case of Erdös-Rényi random graphs. Here we analytically study roots on random graphs. We further show that, with a simple geometrical interpretation and a concise mean-field theory of the GLR procedure, we reproduce the zero-temperature replica symmetric estimation of relative sizes of both minimal vertex covers and maximum matchings on random graphs with or without cores. *

show abstract

Section: Introductionmentioning

confidence: 99%

Two faces of greedy leaf removal procedure on graphs

Zhao¹,

Zhou²

2019

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

“…1): (i) multicriteria problem formulations (e.g., [38,44,47,129,130]), (ii) problems under uncertainty (fuzzy combinatorial optimization problems, etc.) (e.g., [86,96,111,140,142]), (iii) problems in dynamic environments (e.g., [25,106,140,141]), and online problems (e.g., [3,4,28,64]). Evidently, the above-mentioned problem development directions can have intersections (e.g., multicriteria online problem under uncertainty).…”

Section: Introductionmentioning

confidence: 99%

Towards Integrated Glance To Restructuring in Combinatorial Optimization

Levin

2015

Preprint

View full text Add to dashboard Cite

The paper focuses on a new class of combinatorial problems which consists in restructuring of solutions (as sets/structures) in combinatorial optimization. Two main features of the restructuring process are examined: (i) a cost of the restructuring, (ii) a closeness to a goal solution. Three types of the restructuring problems are under study: (a) one-stage structuring, (b) multi-stage structuring, and (c) structuring over changed element set. One-criterion and multicriteria problem formulations can be considered. The restructuring problems correspond to redesign (improvement, upgrade) of modular systems or solutions. The restructuring approach is described and illustrated (problem statements, solving schemes, examples) for the following combinatorial optimization problems: knapsack problem, multiple choice problem, assignment problem, spanning tree problems, clustering problem, multicriteria ranking (sorting) problem, morphological clique problem. Numerical examples illustrate the restructuring problems and solving schemes.

show abstract

“…(see e.g. Chapter 4 in [25] for a survey). For this reason it has been deeply studied since the late 60's (see, e.g., [23]).…”

Section: Introductionmentioning

confidence: 99%

The Feedback Arc Set Problem with Triangle Inequality Is a Vertex Cover Problem

Mastrolilli

2012

LATIN 2012: Theoretical Informatics

View full text Add to dashboard Cite

We consider the (precedence constrained) Minimum Feedback Arc Set problem with triangle inequalities on the weights, which finds important applications in problems of ranking with inconsistent information. We present a surprising structural insight showing that the problem is a special case of the minimum vertex cover in hypergraphs with edges of size at most 3. This result leads to combinatorial approximation algorithms for the problem and opens the road to studying the problem as a vertex cover problem.

show abstract

Fuzzy Combinatorial Optimization Problems

Cited by 7 publications

References 157 publications

Two faces of greedy leaf removal procedure on graphs

Two faces of greedy leaf removal procedure on graphs

Towards Integrated Glance To Restructuring in Combinatorial Optimization

The Feedback Arc Set Problem with Triangle Inequality Is a Vertex Cover Problem

Contact Info

Product

Resources

About