07261 Abstracts Collection -- Fair Division

From 24.06. to 29.06.2007, the Dagstuhl Seminar 07261 % generate automatically ``Fair Division\u27\u27 % generate automatically was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Prior-Independent Mechanisms for Scheduling

We study the makespan minimization problem with unrelated selfish machines under the assumption that job sizes are stochastic. We design simple truthful mechanisms that under various distributional assumptions provide constant and sublogarithmic approximations to expected makespan. Our mechanisms are prior-independent in that they do not rely on knowledge of the job size distributions. Prior-independent approximation mechanisms have been previously studied for the objective of revenue maximization [Dhangwatnotai, Roughgarden and Yan'10, Devanur, Hartline, Karlin and Nguyen'11, Roughgarden, Talgam-Cohen and Yan'12]. In contrast to our results, in prior-free settings no truthful anonymous deterministic mechanism for the makespan objective can provide a sublinear approximation [Ashlagi, Dobzinski and Lavi'09].Comment: This paper will appear in Proceedings of the ACM Symposium on Theory of Computing 2013 (STOC'13

Packing, Scheduling and Covering Problems in a Game-Theoretic Perspective

Many packing, scheduling and covering problems that were previously considered by computer science literature in the context of various transportation and production problems, appear also suitable for describing and modeling various fundamental aspects in networks optimization such as routing, resource allocation, congestion control, etc. Various combinatorial problems were already studied from the game theoretic standpoint, and we attempt to complement to this body of research. Specifically, we consider the bin packing problem both in the classic and parametric versions, the job scheduling problem and the machine covering problem in various machine models. We suggest new interpretations of such problems in the context of modern networks and study these problems from a game theoretic perspective by modeling them as games, and then concerning various game theoretic concepts in these games by combining tools from game theory and the traditional combinatorial optimization. In the framework of this research we introduce and study models that were not considered before, and also improve upon previously known results.Comment: PhD thesi

Fair allocation of operations and makespan minimization for multiple robotic agents

We study the problem of allocating a set of indivisible operations to a set of agents in a fair and efficient manner while also minimizing the makespan. We first present the Operation Trading Algorithm that generates allocations satisfying the DEQx (Duplicated Equitability up to any operation) fairness criterion while also guaranteeing an upper bound of 2 on the makespan for identical agents. The algorithm also guarantees an upper bound of 1.618 for 2 uniformly related agents and (1+√(4n−3))/2 for n uniformly related agents. The pairwise approach used in this algorithm has the added advantages of being decentralizable, reactive and robust. A new protocol named as the Decentralized Random Group Formation (DRGF) Protocol is presented for implementing the Operation Trading Algorithm in a decentralized manner and for dealing with communication failures. We then define a relaxed version of the DEQ1 (Duplicated Equitability upto some operation) fairness criterion called partial-DEQ1. A market-based algorithm is presented to achieve partial-DEQ1 along with Pareto Optimality. Following this, it is shown that the algorithm also guarantees an upper bound of 1.618 on the makespan for 2 non-identical agents. Parametric pruning further improves the upper bound to 1.5, which is theoretically the best possible upper bound. To the best of our knowledge, these are the first algorithms designed to achieve the mentioned fairness criteria. The algorithms additionally guarantee upper bounds on the makespan. Finally, we show the efficacy of the algorithms in generating allocations with near optimal makespans by numerically evaluating the algorithms on randomly generated problem instances