Carlo Mannino

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.

Upward drawings of triconnected digraphs

A polynomial-time algorithm for testing if a triconnected directed graph has an upward drkwing is presented. An upward drkwing is a planar drkwing such that all the edges flow in a common direction (e.g., from bottom to top). The problem arises in the fields of automatic graph drkwing and ordered sets, and has been open for several years. The proposed algorithm is based on a new combinatorial characterization that maps the problem into a max-flow problem on a sparse network; the time complexity isO(n+r2), wheren is the number of vertices andr is the number of sources and sinks of the directed graph. If the directed graph has an upward drkwing, the algorithm allows us to construct one easily.

Optimal Real-Time Traffic Control in Metro Stations

Train movements across railway stations are still operated by human dispatchers. Motivated by an application provided by Azienda Trasporti Milanesi (ATM), the major Italian municipal transport company, we developed a real-time automated traffic control system to operate trains in metro stations. The system optimally controls the trains in a metro station by identifying a suitable routing and by establishing an optimum schedule of the performed operations. For each candidate routing an instance of the blocking, no-wait job-shop scheduling problem with convex costs is solved to optimality by branch and bound. A new, effective lower bound is developed to speed up the enumeration process. Computational testing in a real environment proved that the algorithm is able to solve relevant practical instances within the very tight time limit imposed by the application. The system has been in operation in the Milan metro since July 2007. To our knowledge, this is the first example of successful application of optimization methods to real-time traffic control in metro stations.

Solving hard set covering problems

We propose a new branch-and-bound algorithm to solve hard instances of set covering problems arising from Steiner triple systems.

GUB Covers and Power-Indexed Formulations for Wireless Network Design

We propose a pure 0-1 formulation for the wireless network design problem, i.e., the problem of configuring a set of transmitters to provide service coverage to a set of receivers. In contrast with classical mixed-integer formulations, where power emissions are represented by continuous variables, we consider only a finite set of power values. This has two major advantages: it better fits the usual practice and eliminates the sources of numerical problems that heavily affect continuous models. A crucial ingredient of our approach is an effective basic formulation for the single knapsack problem representing the coverage condition of a receiver. This formulation is based on the generalized upper bound GUB cover inequalities introduced by Wolsey [Wolsey L 1990 Valid inequalities for 0-1 knapsacks and mips with generalised upper bound constraints. Discrete Appl. Math. 292--3:251--261]; and its core is an extension of the exact formulation of the GUB knapsack polytope with two GUB constraints. This special case corresponds to the very common practical situation where only one major interferer is present. We assess the effectiveness of our formulation by comprehensive computational results over realistic instances of two typical technologies, namely, WiMAX and DVB-T. This paper was accepted by Dimitris Bertsimas, optimization.

An enumerative algorithm for the frequency assignment problem

We present an algorithm to solve the frequency assignment problem for mobile cellular systems and radio and television broadcasting. Frequencies must be assigned to transmitters in order to meet interference requirements so that the overall signal/noise ratio is satisfactory. The basic scheme is an exact enumerative method provided with fixing criteria to reduce the size of the instances. Larger instances are solved by applying the algorithm to suitable subinstances, eventually extending the solutions found. We were able to solve large real-life instances arising in radio broadcasting and mobile cellular systems. Computational results outperform previous results reported in the literature.

An exact algorithm for the maximum stable set problem

We describe a new branch-and-bound algorithm for the exact solution of the maximum cardinality stable set problem. The bounding phase is based on a variation of the standard greedy algorithm for finding a colouring of a graph. Two different node-fixing heuristics are also described. Computational tests on random and structured graphs and very large graphs corresponding to ‘real-life’ problems show that the algorithm is competitive with the fastest algorithms known so far.

The implementor/adversary algorithm for the cyclic and robust scheduling problem in health-care

A general problem in health-care consists in allocating some scarce medical resource, such as operating rooms or medical staff, to medical specialties in order to keep the queue of patients as short as possible. A major difficulty stems from the fact that such an allocation must be established several months in advance, and the exact number of patients for each specialty is an uncertain parameter. Another problem arises for cyclic schedules, where the allocation is defined over a short period, e.g. a week, and then repeated during the time horizon. However, the demand typically varies from week to week: even if we know in advance the exact demand for each week, the weekly schedule cannot be adapted accordingly. We model both the uncertain and the cyclic allocation problem as adjustable robust scheduling problems. We develop a row and column generation algorithm to solve this problem and show that it corresponds to the implementor/adversary algorithm for robust optimization recently introduced by Bienstock for portfolio selection. We apply our general model to compute master surgery schedules for a real-life instance from a large hospital in Oslo.

The Network Packing Problem in Terrestrial Broadcasting

The introduction of digital terrestrial broadcasting all over Europe requires a complete and challenging replanning of in-place analog systems. However, an abrupt migration of resources (transmitters and frequencies) from analog to digital networks cannot be accomplished because the analog services must be preserved temporarily. Hence, a multiobjective problem arises, in which several networks sharing a common set of resources have to be designed. This problem is referred to as the network packing problem. In Italy, this problem is particularly challenging because of a large number of transmitters, orographical features, and strict requirements imposed by Italian law. In this paper, we report our experience in developing solution methods at the major Italian broadcaster Radiotelevisione Italiana (RAI S.p.A.). We propose a two-stage heuristic. In the first stage, emission powers are assigned to each network separately. In the second stage, frequencies are assigned to all networks so as to minimize the loss from mutual interference. A software tool incorporating our methodology is currently in use at RAI to help discover and select high-quality alternatives for the deployment of digital equipment.

Optimization Problems and Models for Planning Cellular Networks

During the last decade the tremendous success of mobile phone systems has triggered considerable technological advances as well as the investigation of mathematical models and optimization algorithms to support planning and management decisions. In this chapter, we give an overview of some of the most significant optimization problems arising in planning second and third generation cellular networks, we describe the main corresponding mathematical models, and we briefly mention some of the computational approaches that have been devised to tackle them. For second generation systems (GSM), the planning problem can be subdivided into two distinct subproblems: coverage planning, in which the antennas are located so as to maximize service coverage, and capacity planning, in which frequencies are assigned to the antennas so as to maximize a measure of the overall quality of the received signals. For third generation systems (UMTS) network planning is even more challenging, since, due to the peculiarities of the radio interface, coverage and capacity issues must be simultaneously addressed.