Leen Stougie

A stochastic method for global optimization

A stochastic method for global optimization is described and evaluated. The method involves a combination of sampling, clustering and local search, and terminates with a range of confidence intervals on the value of the global optimum. Computational results on standard test functions are included as well.

Multiprocessor Scheduling with Rejection

We consider a version of multiprocessor scheduling with the special feature that jobs may be rejected at a certain penalty. An instance of the problem is given by m identical parallel machines and a set of n jobs, with each job characterized by a processing time and a penalty. In the on-line version the jobs become available one by one and we have to schedule or reject a job before we have any information about future jobs. The objective is to minimize the makespan of the schedule for accepted jobs plus the sum of the penalties of rejected jobs. The main result is a 1 + 2:618 competitive algorithm for the on-line version of the problem, where is the golden ratio. A matching lower bound shows that this is the best possible algorithm working for all m. For xed m we give improved bounds; in particular, for m = 2 we give a 1:618 competitive algorithm, which is best possible. For the o-line problem we present a fully polynomial approximation scheme for xed m and a polynomial approximation scheme for arbitrarym. Moreover, we present an approximation algorithm which runs in time O(n logn) for arbitrary m and guarantees a 2i 1 m approximation ratio.

Ancient Dispersal of the Human Fungal Pathogen Cryptococcus gattii from the Amazon Rainforest

Over the past two decades, several fungal outbreaks have occurred, including the high-profile ‘Vancouver Island’ and ‘Pacific Northwest’ outbreaks, caused by Cryptococcus gattii, which has affected hundreds of otherwise healthy humans and animals. Over the same time period, C. gattii was the cause of several additional case clusters at localities outside of the tropical and subtropical climate zones where the species normally occurs. In every case, the causative agent belongs to a previously rare genotype of C. gattii called AFLP6/VGII, but the origin of the outbreak clades remains enigmatic. Here we used phylogenetic and recombination analyses, based on AFLP and multiple MLST datasets, and coalescence gene genealogy to demonstrate that these outbreaks have arisen from a highly-recombining C. gattii population in the native rainforest of Northern Brazil. Thus the modern virulent C. gattii AFLP6/VGII outbreak lineages derived from mating events in South America and then dispersed to temperate regions where they cause serious infections in humans and animals.

On-line single-server dial-a-ride problems

In this paper results on the dial-a-ride problem with a single server are presented. Requests for rides consist of two points in a metric space, a source and a destination. A ride has to be made by the server from the source to the destination. The server travels at unit speed in the metric space and the objective is to minimize some function of the delivery times at the destinations. We study this problem in the natural on-line setting. Calls for rides come in while the server is traveling. This models e.g. the taxi problem, or, if the server has capacity more than 1 a minibus or courier service problem. For the version of this problem in which the server has infinite capacity having as objective minimization of the time the last destination is served, we design an algorithm that has competitive ratio 2. We also show that this is best possible, since no algorithm can have competitive ratio better than 2 independently of the capacity of the servers. Besides, we give a simple 2.5-competitive algorithm for the case with finite capacity. Then we study the on-line problem with objective minimization of the sum of completion times of the rides. We prove a lower bound on the competitive ratio of any algorithm of 1 + \sqrt{2} for a server with any capacity and of 3 for a server with capacity 1. Finally, we present the first competitive algorithm for the case the server has infinite capacity and the metric space is the real line. The algorithm has competitive ratio 15. Keywords: Dial-a-ride, on-line optimization, competitive analysis.

The Preemptive Uniprocessor Scheduling of Mixed-Criticality Implicit-Deadline Sporadic Task Systems

Systems in many safety-critical application domains are subject to certification requirements. For any given system, however, it may be the case that only a subset of its functionality is safety-critical and hence subject to certification, the rest of the functionality is non safety critical and does not need to be certified, or is certified to a lower level of assurance. An algorithm called EDF-VD (for Earliest Deadline First with Virtual Deadlines) is described for the scheduling of such mixed-criticality task systems. Analyses of EDF-VD significantly superior to previously-known ones are presented, based on metrics such as processor speedup factor (EDF-VD is proved to be optimal with respect to this metric) and utilization bounds.

Networks: expanding evolutionary thinking

Networks allow the investigation of evolutionary relationships that do not fit a tree model. They are becoming a leading tool for describing the evolutionary relationships between organisms, given the comparative complexities among genomes.

Solving stochastic programs with integer recourse by enumeration: a framework using Gro¨bner basis reductions

In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Gröbner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the expected integer recourse function, we prove that under mild conditions an optimal solution is contained in a finite set. Furthermore, we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed.

Modes and cuts in metabolic networks: Complexity and algorithms

Constraint-based approaches recently brought new insight into our understanding of metabolism. By making very simple assumptions such as that the system is at steady-state and some reactions are irreversible, and without requiring kinetic parameters, general properties of the system can be derived. A central concept in this methodology is the notion of an elementary mode (EM for short) which represents a minimal functional subsystem. The computation of EMs still forms a limiting step in metabolic studies and several algorithms have been proposed to address this problem leading to increasingly faster methods. However, although a theoretical upper bound on the number of elementary modes that a network may possess has been established, surprisingly, the complexity of this problem has never been systematically studied. In this paper, we give a systematic overview of the complexity of optimisation problems related to modes. We first establish results regarding network consistency. Most consistency problems are easy, i.e., they can be solved in polynomial time. We then establish the complexity of finding and counting elementary modes. We show in particular that finding one elementary mode is easy but that this task becomes hard when a specific EM (i.e. an EM containing some specified reactions) is sought. We then show that counting the number of elementary modes is musical sharpP-complete. We emphasize that the easy problems can be solved using currently existing software packages. We then analyse the complexity of a closely related task which is the computation of so-called minimum reaction cut sets and we show that this problem is hard. We then present two positive results which both allow to avoid computing EMs as a prior to the computation of reaction cuts. The first one is a polynomial approximation algorithm for finding a minimum reaction cut set. The second one is a test for verifying whether a set of reactions constitutes a reaction cut; this test can be readily included in existing algorithms to improve their performance. Finally, we discuss the complexity of other cut-related problems.

A Generalized Parallel Task Model for Recurrent Real-time Processes

A model is considered for representing recurrent precedence-constrained tasks that are to execute on multiprocessor platforms. A recurrent task is specified as a directed a cyclic graph (DAG), a period, and a relative deadline. Each vertex of the DAG represents a sequential job, while the edges of the DAG represent precedence constraints between these jobs. All the jobs of the DAG are released simultaneously and need to complete execution within the specified relative deadline of their release. The task may release jobs in this manner an unbounded number of times, with successive releases occurring at least the specified period apart. The scheduling problem is to determine whether such a recurrent task can be scheduled to always meet all deadlines upon a specified number of processors that are dedicated for the use of this task. This problem is shown to be computationally intractable, but amenable to efficient approximate solutions. EDF is shown to be a good approximate scheduling algorithm. Polynomial and pseudo-polynomial schedulability tests, of differing effectiveness, are presented for determining whether a given task can be scheduled by EDF to always meet all deadlines on a specified number of processors.

News from the Online Traveling Repairman

In the traveling repairman problem (TRP), a tour must be found through every one of a set of points (cities) in some metric space such that the weighted sum of completion times of the cities is minimized. Given a tour, the completion time of a city is the time traveled on the tour before the city is reached. In the online traveling repairman problem OLTRP requests for visits to cities arrive online while the repairman is traveling. We analyze the performance of algorithms for the online problem using competitive analysis, where the cost of an online algorithm is compared to that of an optimal offline algorithm. Feuerstein and Stougie [8] present a 9-competitive algorithm for the OlTrp on the real line. In this paper we show how to use techniques from online-scheduling to obtain a 6-competitive deterministic algorithm for the OlTrp on any metric space. We also present a randomized algorithm with competitive ratio of 3/ln 2 2.1282 for the L-OLDARP on the line, 4e-5/2e-3 > 2.41041 for the L-OLDARP on general metric spaces, 2 for the OLTRP on the line, and 7/3 for the OLTRP on general metric spaces.