The Set Covering Problem SCP is a main model for several important applications including crew scheduling in railway and mass transit companies In this survey we focus our attention on the most recent and e ective algo rithms for SCP considering both heuristic and exact approaches outlining their main characteristics and presenting an experimental comparison on the test bed instances of Beasley...

We develop a novel framework, the implicit hitting set approach, for solving a class of combinatorial optimization problems. The explicit hitting set problem is as follows: given a set U and a family S of subsets of U , find a minimum-cardinality set that intersects (hits) every set in S. In the implicit hitting set problem (IHSP), the family of subsets S is not explicitly listed (its size is, ...

In an implicit combinatorial optimization problem, the constraints are not enumerated explicitly but rather stated implicitly through equations, other constraints or auxiliary algorithms. An important subclass of such problems is the implicit set cover (or, equivalently, hitting set) problem in which the sets are not given explicitly but rather defined implicitly For example, the well-known min...

In an implicit combinatorial optimization problem, the constraints are not enumerated explicitly but rather stated implicitly through equations, other constraints or auxiliary algorithms. An important subclass of such problems is the implicit set cover (or, equivalently, hitting set) problem in which the sets are not given explicitly but rather defined implicitly For example, the well-known min...

Similarly to Maximum Satisfiability (MaxSAT), Minimum Satisfiability (MinSAT) is an optimization extension of the Boolean Satisfiability (SAT) decision problem. In recent years, both problems have been studied in terms of exact and approximation algorithms. In addition, the MaxSAT problem has been characterized in terms of Maximal Satisfiable Subsets (MSSes) and Minimal Correction Subsets (MCSe...

By definition, web-services composition works on developing merely optimum coordination among a number of available web-services to provide a new composed web-service intended to satisfy some users requirements for which a single web service is not (good) enough. In this article, the formulation of the automatic web-services composition is proposed as several set-cover problems and an approxima...

Classical minimum entropy set cover problem relies on the finding the most likely assignment between the set of observations and the given set of their types. The solution is described by such partition of data space which minimizes the entropy of the distribution of types. The problem finds a natural application in the machine learning, clustering and data classification. In this paper we show...

We present a packing-based approximation algorithm for the k-Set Cover problem. We introduce a new local search-based k-set packing heuristic, and call it Restricted k-Set Packing. We analyze its tight approximation ratio via a complicated combinatorial argument. Equipped with the Restricted k-Set Packing algorithm, our k-Set Cover algorithm is composed of the k-Set Packing heuristic [7] for k ...

In this paper, we study the computational complexity and approximation complexity of the connected set-cover problem. We derive necessary and sufficient conditions for the connected set-cover problem to have a polynomial-time algorithm. We also present a sufficient condition for the existence of a (1 + ln δ)-approximation. In addition, one such (1 + ln δ)-approximation algorithm for this proble...

The infrastructure for mobile distributed tasks is often formed by cellular networks. One of the major issues in such networks is interference. In this paper we tackle interference reduction by suitable assignment of transmission power levels to base stations. This task is formalized introducing the Minimum Membership Set Cover combinatorial optimization problem. On the one hand we prove that i...