Antonio Sassano

Models and solution techniques for frequency assignment problems

Abstract Wireless communication is used in many different situations such as mobile telephony, radio and TV broadcasting, satellite communication, wireless LANs, and military operations. In each of these situations a frequency assignment problem arises with application specific characteristics. Researchers have developed different modeling ideas for each of the features of the problem, such as the handling of interference among radio signals, the availability of frequencies, and the optimization criterion. This survey gives an overview of the models and methods that the literature provides on the topic. We present a broad description of the practical settings in which frequency assignment is applied. We also present a classification of the different models and formulations described in the literature, such that the common features of the models are emphasized. The solution methods are divided in two parts. Optimization and lower bounding techniques on the one hand, and heuristic search techniques on the other hand. The literature is classified according to the used methods. Again, we emphasize the common features, used in the different papers. The quality of the solution methods is compared, whenever possible, on publicly available benchmark instances.

A Lagrangian-based heuristic for large-scale set covering problems

We present a new Lagrangian-based heuristic for solving large-scale set-covering problems arising from crew-scheduling at the Italian Railways (Ferrovie dello Stato). Our heuristic obtained impressive results when compared to state-of-the-art codes on a test-bed provided by the company, which includes instances with sizes ranging from 50,000 variables and 500 constraints to 1,000,000 variables and 5000 constraints.

Computational study of large-scale p -Median problems

Given a directed graph G(V,A), the p-Median problem consists of determining p nodes (the median nodes) minimizing the total distance from the other nodes of the graph. We present a Branch-and-Cut-and-Price algorithm yielding provably good solutions for instances with |V|≤3795. Key ingredients of the algorithm are a delayed column-and-row generation technique, exploiting the special structure of the formulation, to solve the LP-relaxation, and cutting planes to strengthen the formulation and limit the size of the enumeration tree.

Scheduling tasks with sequence-dependent processing times

In this article we consider the problem of minimizing the maximum completion time of a sequence of n jobs on a single machine. Nonzero ready times and sequence-dependent processing times are allowed. Upper bounds, lower bounds, and dominance criteria are proposed and exploited in a branch-and-bound algorithm. Computational results are given.

On the facial structure of the set covering polytope dimensional linear programming

AbstractGiven a bipartite graphG = (V, U, E), a cover ofG is a subset

On the p-Median polytope

D \subseteq V

The Rank Facets of the Stable Set Polytope for Claw-Free Graphs

with the property that each nodeu ∈ U is adjacent to at least one nodev ∈D. If a positive weightcv is associated with each nodev ∈V, the covering problem (CP) is to find a cover ofG having minimum total weight.In this paper we study the properties of the polytopeQ(G) ⊂ ℝ|V|, the convex hull of the incidence vectors of all the covers inG. After discussing some general properties ofQ(G) we introduce a large class of bipartite graphs with special structure and describe several types of rank facets of the associated polytopes.Furthermore we present two lifting procedures to derive valid inequalities and facets of the polytopeQ(G) from the facets of any polytopeQ(G′) associated with a subgraphG′ ofG. An example of the application of the theory to a class of hard instances of the covering problem is also presented.

The equipartition polytope. I: formulations, dimension and basic facets

In this paper, we consider inequalities of the formΣ αjxj ≥ β, whereαj equals 0 or 1, andβ is a positive integer. We give necessary and sufficient conditions for such inequalities to define facets of the set covering polytope associated with a 0, 1 constraint matrixA. These conditions are in terms of critical edges and critical cutsets defined in the bipartite incidence graph ofA, and are in the spirit of the work of Balas and Zemel on the set packing problem where similar notions were defined in the intersection graph ofA. Furthermore, we give a polynomial characterization of a class of 0, 1 facets defined from chorded cycles of the bipartite incidence graph. This characterization also yields all the 0, 1 liftings of odd-hole inequalities for the simple plant location polytope.