AbstractÐScheduling jobs on the IBM SP2 system and many other distributed-memory MPPs is usually done by giving each job a partition of the machine for its exclusive use. Allocating such partitions in the order in which the jobs arrive (FCFS scheduling) is fair and predictable, but suffers from severe fragmentation, leading to low utilization. This situation led to the development of the EASY scheduler which uses aggressive backfilling: Small jobs are moved ahead to fill in holes in the schedule, provided they do not delay the first job in the queue. We compare this approach with a more conservative approach in which small jobs move ahead only if they do not delay any job in the queue and show that the relative performance of the two schemes depends on the workload: For workloads typical on SP2 systems, the aggressive approach is indeed better, but, for other workloads, both algorithms are similar. In addition, we study the sensitivity of backfilling to the accuracy of the runtime estimates provided by the users and find a very surprising result: Backfilling actually works better when users overestimate the runtime by a substantial factor.

This paper analyzes incentive compatible (truthful) mechanisms over restricted domains of preferences, the leading example being combinatorial auctions. Our work generalizes the characterization of Roberts (1979) who showed that truthful mechanisms over unrestricted domains with at least 3 possible outcomes must be "affine maximizers". We show that truthful mechanisms for combinatorial auctions (and related restricted domains) must be "almost affine maximizers" if they also satisfy an additional requirement of "independence of irrelevant alternatives". This requirement is without loss of generality for unrestricted domains as well as for auctions between two players where all goods must be allocated. This implies unconditional results for these cases, including a new proof of Roberts' theorem. The computational implications of this characterization are severe, as reasonable "almost affine maximizers" are shown to be as computationally hard as exact optimization. This implies the near-helplessness of such truthful polynomial-time auctions in all cases where exact optimization is computationally intractable.

We characterize dominant-strategy incentive compatibility with multidimensional types. A deterministic social choice function is dominant-strategy incentive compatible if and only if it is weakly monotone (W-Mon). The W-Mon requirement is the following: If changing one agent's type (while keeping the types of other agents fixed) changes the outcome under the social choice function, then the resulting difference in utilities of the new and original outcomes evaluated at the new type of this agent must be no less than this difference in utilities evaluated at the original type of this agent.

When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCG-like payment rules will not ensure truthfulness).We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann O'Callaghan, and Shoham, who presented greedy heuristics, and show how to use IF-THEN-ELSE constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios.

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