Carlos A. S. Oliveira

A survey of combinatorial optimization problems in multicast routing

In multicasting routing, the main objective is to send data from one or more sources to multiple destinations, while at the same time minimizing the usage of resources. Examples of resources which can be minimized include bandwidth, time and connection costs. In this paper, we survey applications of combinatorial optimization to multicast routing. We discuss the most important problems considered in this area, as well as their models. Algorithms for each of the main problems are also presented.

A New Heuristic for the Minimum Connected Dominating Set Problem on Ad Hoc Wireless Networks

Given a graph G = (V, E), a dominating set D is a subset of V such that any vertex not in D is adjacent to at least one vertex in D. Efficient algorithms for computing the minimum connected dominating set (MCDS) are essential for solving many practical problems, such as finding a minimum size backbone in ad hoc networks. Wireless ad hoc networks appear in a wide variety of applications, including mobile commerce, search and discovery, and military battlefield. In this chapter we propose a new efficient heuristic algorithm for the minimum connected dominating set problem. The algorithm starts with a feasible solution containing all vertices of the graph. Then it reduces the size of the CDS by excluding some vertices using a greedy criterion. We also discuss a distributed version of this algorithm. The results of numerical testing show that, despite its simplicity, the proposed algorithm is competitive with other existing approaches.

GRASP with Path-Relinking for the Quadratic Assignment Problem

This paper describes a GRASP with path-relinking heuristic for the quadratic assignment problem. GRASP is a multi-start procedure, where different points in the search space are probed with local search for high-quality solutions. Each iteration of GRASP consists of the construction of a randomized greedy solution, followed by local search, starting from the constructed solution. Path-relinking is an approach to integrate intensification and diversification in search. It consists in exploring trajectories that connect high-quality solutions. The trajectory is generated by introducing in the initial solution, attributes of the guiding solution. Experimental results illustrate the effectiveness of GRASP with path-relinking over pure GRASP on the quadratic assignment problem.

Optimization techniques for string selection and comparison problems in genomics

In this article, a discussion of optimization issues occurring in the area of genomics such as string comparison and selection problems are discussed. With this objective, an important part of the existing results in this area will be discussed. The problems that are of interest in this paper include the closest string problem (CSP), closest substring problem (CSSP), farthest string problem (FSP), farthest substring problem (FSSP), and far from most string (FFMSP) problem. The paper presents a detailed view of the most important problems occurring in the area of string comparison and selection, using the Hamming distance measure is given.

Optimization Problems in Multicast Tree Construction

Multicasting is a technique for data routing in networks that allows multiple destinations to be addressed simultaneously. The implementation of multicasting requires, however, the solution of difficult combinatorial optimization problems. In this chapter, we discuss combinatorial issues occurring in the implementation of multicast routing, including multicast tree construction, minimization of the total message delay, center-based routing, and multicast message packing. Optimization methods for these problems are discussed and the corresponding literature reviewed. Mathematical programming as well as graph models for these problems are discussed.

Reactive GRASP with path relinking for channel assignment in mobile phone networks

The Frequency Assignment Problem (FAP) arises in wireless networks when the number of available frequency channels is smaller than the number of users. FAP is NP-hard and plays an important role in the network planning. Usually, the number of available channels is much smaller than the number of users accessing the wireless network. In this case, the reuse of frequency channels is mandatory. Consequently, this may cause interference. Nowadays, cellular phone operators use various techniques designed to cope with channel shortage and, as a consequence, to avoid interference. For instance, frequency division by time or code, and local frequency clustering models have been used. These techniques are bounded by the number of users, i.e. as the number of users increases, they tend to become obsolete. In this work, we propose to minimize the total interference of the system, using a metaheuristic based on GRASP (Greedy Randomized Adaptive Search Procedure). A reactive heuristic has been used in order to automatically balance GRASP parameters. Furthermore, Path Relinking, which consists of an intensification strategy, has been applied. We report experimental results given by our proposed approach.

A combinatorial algorithm for message scheduling on controller area networks

A controller area network (CAN) is a special-purpose communications system, used for real time control of embedded components in vehicles and other general purpose automation systems. A combinatorial algorithm based on network optimisation concepts is presented for scheduling messages on a CAN. The message scheduling (CANMS) problem in CAN requires that messages be allocated according to their priorities, to prevent excessive delays on important messages. The CANMS is an NP-hard problem. The objective of the proposed algorithm is to minimise the total time allocated for message occurrences, in order to avoid message loss. A graph construction is employed, transforming the original problem into the problem of finding cliques with restricted size. According to computer experiments conducted on representative instances, low latency schedules can be obtained through the use of the proposed algorithm. The low computational complexity of the procedure presents the possibility of efficiently solving larger instances of this NP-hard problem.

On the number of local minima for the multidimensional assignment problem

The Multidimensional Assignment Problem (MAP) is an NP-hard combinatorial optimization problem occurring in many applications, such as data association, target tracking, and resource planning. As many solution approaches to this problem rely, at least partly, on local neighborhood search algorithms, the number of local minima affects solution difficulty for these algorithms. This paper investigates the expected number of local minima in randomly generated instances of the MAP. Lower and upper bounds are developed for the expected number of local minima, E[M], in an MAP with iid standard normal coefficients. In a special case of the MAP, a closed-form expression for E[M] is obtained when costs are iid continuous random variables. These results imply that the expected number of local minima is exponential in the number of dimensions of the MAP. Our numerical experiments indicate that larger numbers of local minima have a statistically significant negative effect on the quality of solutions produced by several heuristic algorithms that involve local neighborhood search.

A distributed optimization algorithm for power control in wireless ad hoc networks

Summary form only given. Power control is an important issue in wireless networks, which still has no satisfactory solution. Due to the limited amount of power available to wireless units, there is a need for systems that operate with reduced power consumption levels. We propose a new model for the problem, that exploits the relationship among necessary power and reach of broadcast. The resulting model is called the power control problem in ad hoc networks (PCADHOC). We derive a linear integer programming model, which is used to find lower bounds on the amount of required power. The constraints of the problem guarantee that all required transmissions can be successfully performed. A distributed algorithm based on variable neighborhood search is proposed to solve the PCADHOC. The results of experiments with the algorithm show that the power savings are considerable.

Revised GRASP with path-relinking for the linear ordering problem

The linear ordering problem (LOP) is an