Submodular functions and related polyhedra play an increasing role in combinatorial optimization. The present survey-type paper is intended to provide a brief account of this theory along with several applications in graph theory and combinatorial optimization.

The paper deals with problems and ultramodern approaches recommended to solve various combinatorial optimization (CO) tasks, by using different types of computing environments, including various clouds (CC). A lot of new ideas have been proposed or at least outlined. Non-standard evaluation of the goal function value is also considered.

Metaheuristics are generic search strategies that can be adapted to solve complex problems. This paper describes in simple terms the most popular metaheuristics for combinatorial optimization problems. It also emphasizes the main contributions of the Canadian research community in the development and application of metaheuristics.

The orienteering problem (OP) is a well established problem in combinatorial optimization. In this problem, there is a set of n nodes or cities, V , and each node i has an associated non-negative score S(i). If a city is visited on a route, then its score is gathered (but visiting a city more than once does not yield additional scoring). Hence, the score associated with a path visiting a set of...

The paper addresses a new class of combinatorial problems which consist in restructuring of solutions (as 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. This problem corresponds to redesign (improvement, upgrade) of modular systems or solutions. The restructuring approa...

Integer optimization problems are concerned with the efficient allocation of limited resources to meet a desired objective when some of the resources in question can only be divided into discrete parts. In such cases, the divisibility constraints on these resources, which may be people, machines, or other discrete inputs, may restrict the possible alternatives to a finite set. Nevertheless, the...

Combinatorial Optimization is an important area of computer science that has many theoretical and practical applications. In this thesis, we present important contributions to several different areas of combinatorial optimization, including nogood learning, symmetry breaking, dominance, relaxations and parallelization. We develop a new nogood learning technique based on constraint projection th...

2007 Preface This a continually updated version of my second PhD thesis, submitted to the Department of Applied Mathematics at Charles University. It serves mainly for myself as a compendium of my research on submodular optimization and related problems, Acknowledgement This thesis would not have seen the light of day without the support and perseverance of Martin Loebl, and significant assista...

This overview surveys two general methods for establishing limit theorems for functionals in discrete stochastic geometry. The functionals of interest are linear statistics with the general representation ∑x∈X ξ (x,X ), where X is locally finite and where the interactions of x with respect to X , given by ξ (x,X ), exhibit spatial dependence. We focus on subadditive methods and stabilization me...