Evripidis Bampis

A Dynasearch Neighborhood for the Bicriteria Traveling Salesman Problem

In this paper we extend the dynasearch approach proposed by Congram, Potts and van de Velde [4, 17] in the context of multicriteria optimization for the bicriteria traveling salesman problem. The idea is to use local search with an exponential sized neighborhood which can be searched in polynomial time using dynamic programming and a rounding technique. Experimental results are presented to verify the quality of the proposed approach to obtain approximate Pareto curves for the bicriteria traveling salesman problem.

On the approximate tradeoff for bicriteria batching and parallel machine scheduling problems

We consider multiobjective scheduling problems, i.e. scheduling problems that are evaluated with respect to many cost criteria, and we are interested in determining a trade-off (Pareto curve) among these criteria. We study two types of bicriteria scheduling problems: single-machine batching problems and parallel machine scheduling problems. Instead of proceeding in a problem-by-problem basis, we identify a class of multiobjective optimization problems possessing a fully polynomial time approximation scheme (FPTAS) for computing an ?-approximate Pareto curve. This class contains a set of problems whose Pareto curve can be computed via a simple pseudo-polynomial dynamic program for which the objective and transition functions satisfy some, easy to verify, arithmetical conditions. Our study is based on a recent work of Woeginger (Electronic Colloquium on Computational Complexity, Report 84 (short version appeared in SODA?99, pp. 820?829)) for the single criteria optimization ex-benevolent problems. We show how our general result can be applied to the considered scheduling problems.

Scheduling in Switching Networks with Set-Up Delays

We consider the (preemptive bipartite scheduling problem PBS) (Crescenzi et al., “On approximating a scheduling problem,” Journal of Combinatorial Optimization, vol. 5, pp. 287–297, 2001) arising in switching communication systems, where each input and output port can be involved in at most one communication at the same time. Given a set of communication tasks to be communicated from the transmitters to the receivers of such a system, we aim to find a schedule minimizing the overall transmission time. To achieve this, we allow the preemption of communication tasks. However, in practice preemption comes with a cost, d, and this renders the problem NP-hard (Gopal et al., “An optimal switching algorithm for multibeam satellite systems with variable bandwidth beams,” IEEE Trans. Commun., vol.30, pp. 2475–2481, 1982). In this paper, we present a

Bicriteria approximation algorithms for scheduling problems with communications delays

2 - \frac{1}{d+1}

The price of approximate stability for scheduling selfish tasks on two links

approximation algorithm, which is the first one for the PBS problem with approximation ratio strictly less than two. Furthermore, we propose a simple optimal polynomial time algorithm for a subclass of instances of the PBS problem.

On-Line bicriteria interval scheduling

Many papers deal with the approximability of multi-criteria optimization problems but only a small number of non-approximability results, which rely on NP-hardness, exist in the literature. In this paper, we provide a new way of proving non-approximability results which relies on the existence of a small size good approximating set (i.e. it holds even in the unlikely event of P=NP). This method may be used for several problems but here we illustrate it for a multi-criteria version of the traveling salesman problem with distances one and two (TSP(1,2)). Following the article of Angel et al. (FCT 2003) who presented an approximation algorithm for the bi-criteria TSP(1,2), we extend and improve the result to any number k of criteria.

Truthfulness for the Sum of Weighted Completion Times

We study the problem of simultaneously minimizing the makespan and the average weighted completion time for the precedence multiprocessor constrained scheduling problem with unit execution times and unit communication delays, known as the UET–UCT problem (Munier and König, Operations Research, 45(1), 145–148 (1997)). We propose a simple (16/9, 16/9)-approximation algorithm for the problem with an unrestricted number of machines. We improve our algorithm by adapting a technique first introduced by Aslam et al. (Proceedings of ACM-SODA, pp. 846–847, 1999) and provide a (1.745, 1.745)-approximate solution. For the considered scheduling problem, we prove the existence of a (1.445, 1.445)-approximate solution, improving the generic existence result of Aslam et al. (Proceedings of ACM-SODA, pp. 846–847, 1999). Also notice that our results for the case of an unrestricted number of processors hold for the more general scheduling problem with small communication delays (SCT problem), and for two other classical optimality criteria: maximum lateness and weighted lateness. Finally, we propose an approximation algorithm for the UET–UCT problem with a restricted number of processors.

Bicriteria scheduling for contiguous and non contiguous parallel tasks

We consider the traffic grooming problem in passive WDM star networks. Traffic grooming is concerned with the development of techniques for combining low speed traffic components onto high speed channels in order to minimize network cost. We first prove that the traffic grooming problem in star networks is NP-hard for a more restricted case than the one considered in [2]. Then, we propose a polynomial time algorithm for the special case where there are two wavelengths per fiber using matching techniques. Furthermore, we propose two reductions of our problem to two combinatorial optimization problems, the constrained multiset multicover problem [3], and the demand matching problem [4] allowing us to obtain a polynomial time H 2C (resp. \(2+\frac{4}{5}\)) approximation algorithm for the minimization (resp. maximization) version of the problem, where C is the capacity of each wavelength.