We consider algorithmic problems in a distributed setting where the participants cannot be assumed to follow the algorithm but rather their own self-interest. As such participants, termed agents, are capable of manipulating the algorithm, the algorithm designer should ensure in advance that the agents ’ interests are best served by behaving correctly. Following notions from the field of mechanism design, we suggest a framework for studying such algorithms. Our main technical contribution concerns the study of a representative task scheduling problem for which the standard mechanism design tools do not suffice. Journal of Economic Literature

We consider the following scheduling problem. There are m parallel machines and n independent.jobs. Each job is to be assigned to one of the machines. The processing of.job j on machine i requires time Pip The objective is to lind a schedule that minimizes the makespan. Our main result is a polynomial algorithm which constructs a schedule that is guaranteed to be no longer than twice the optimum. We also present a polynomial approximation scheme for the case that the number of machines is fixed. Both approximation results are corollaries of a theorem about the relationship of a class of integer programming problems and their linear programming relaxations. In particular, we give a polynomial method to round the fractional extreme points of the linear program to integral points that nearly satisfy the constraints. In contrast to our main result, we prove that no polynomial algorithm can achieve a worst-case ratio less than ~ unless P = NP. We finally obtain a complexity classification for all special cases with a fixed number of processing times.

We consider the problem of scheduling n jobs with release dates on m machines so as to minimize their average weighted completion time. We present the first known polynomial time approximation schemes for several variants of this problem. Our results include PTASs for the case of identical parallel machines and a constant number of unrelated machines with and without preemption allowed. Our schemes are efficient: for all variants the running time for a (1 + ffl) approximation is of the form f(1=ffl; m)poly(n).

We consider the problem of routing n users on m parallel links, under the restriction that each user may only be routed on a link from a certain set of allowed links for the user. Thus, the problem is equivalent to the correspondingly restricted problem of assigning n jobs to m parallel machines. In a pure Nash equilibrium, no user may improve its own individual cost (delay) by unilaterally switching to another link from its set of allowed links. As our main result, we introduce a polynomial time algorithm to compute from any given assignment a pure Nash equilibrium with non-increased makespan. The algorithm gradually changes a given assignment by pushing unsplittable user traffics through a network that is defined by the users and the links. Here, we use ideas from blocking flows. Furthermore, we use similar techniques as in the generic Preflow-Push algorithm to approximate a schedule with minimum makespan, gaining an improved approximation factor of 2 − 1 for identical links, where w1 is the largest user traffic. w1 We extend this result to related links, gaining an approximation factor of 2. Our approximation algorithms run in polynomial time. We close with tight upper bounds on the coordination ratio for pure Nash equilibria.

We discuss what we consider to be the ten most vexing open questions in the area of polynomial time approximation algorithms for NP-hard deterministic machine scheduling problems. We summarize what is known on these problems, we discuss related results, and we provide pointers to the literature.

Parallel programs may be represented as a set of interrelated sequential tasks. When multiprocessors are used to execute such programs, the parallel portion of the application can be speeded up by an appropriate allocation of processors to the tasks of the application. Given a parallel application defined by a task precedence graph, the goal of task scheduling (or processor assignment) is thus the minimization of the makespan of the application. In a heterogeneous multiprocessor system, task scheduling consists in determining which tasks will be assigned to each processor, as well as the execution order of the tasks assigned to each processor. In this work, we apply the tabu search metaheuristic to the solution of the task scheduling problem on a heterogeneous multiprocessor environment under precedence constraints. The topology of the Mean Value Analysis solution package for product form queueing networks is used as the framework for performance evaluation. We show that tabu search ob...

We consider the problem of scheduling n independent jobs on m unrelated parallel machines, where each job has to be processed by exactly one machine, processing job j on machine i requires p ij time units, and the objective is to minimize the makespan, i.e. the maximum job completion time. Focusing on the case when m is xed, we present for both preemptive and non-preemptive variants of the problem fully polynomial approximation schemes whose running times depend only linearly on n. We also study an extension of the problem, where processing job j on machine i incurs a cost of c ij , and thus there are two optimization criteria: makespan and cost. We show that for any xed m, there is a fully polynomial approximation scheme that, given values T and C, computes for any xed > 0 a schedule in O(n) time with makespan at most (1 + )T and cost at most (1 + )C, if there exists a schedule of makespan T and cost C. 1 Introduction Let n and m denote the number of jobs and machines, respect...

Abstract. In a combinatorial auction k different items are sold to n bidders, where the objective of the seller is to maximize the revenue. The main difficulty to find an optimal allocation is due to the fact that the valuation function of each bidder for bundles of items is not necessarily an additive function over the items. An auction with budget constraints is a common special case where bidders generally have additive valuations, yet they have a limit on their maximal valuation. Auctions with budget constraints were analyzed by Lehmann, Lehmann and Nisan [11], as part of a wider class of auctions, where they have shown that maximizing the revenue is NP-hard, and presented a greedy 2-approximation algorithm. In this paper we present exact and approximate algorithms for auctions with budget constraints. We present a randomized algorithm with an e approximation ratio of ≈ 1.582, which can be derandomized. We e−1 analyze the special case where all bidders have the same budget constraint, and show an algorithm whose approximation ratio is between 1.3837 and 1.3951. We also present an FPTAS for the case of a constant number of bidders. 1

Abstract We consider the problem of scheduling jobs on related machines owned by selfish agents. Pre-viously, Archer and Tardos showed a 2-approximation randomized mechanism which is truthful in expectation only (a weaker notion of truthfulness). We provide a 5-approximation determin-istic truthful mechanism, the first deterministic truthful result for the problem. In case the number of machines is constant, we provide a deterministic Fully PolynomialTime Approximation Scheme (FPTAS) algorithm, and a suitable payment scheme that yields a truthful mechanism for the problem. This result, which is based on converting FPTAS to mono-tone FPTAS, improves a previous result of Auletta et al, who showed a (4 + ")-approximationtruthful mechanism.

We consider the problem of scheduling jobs on parallel related machines owned by selfish agents. We provide deterministic polynomial-time (2+ε)-approximation algorithms and suitable payment functions that yield truthful mechanisms for several NP-hard restrictions of this problem. Up to our knowledge, our result is the first non-trivial polynomial-time deterministic truthful mechanism for this NP-hard problem. Our result also yields a family of deterministic polynomial-time truthful (4+ε)-approximation mechanisms for any fixed number of machines. The only