No abstract

We consider the problem of scheduling jobs on related machines owned by selfish agents. Previously, 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 deterministic truthful mechanism, the first deterministic truthful result for the problem.In case the number of machines is constant, we provide a deterministic Fully Polynomial Time 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 monotone FPTAS, improves a previous result of Auletta et al, who showed a (4 + ε)-approximation truthful mechanism.

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 approximation ratio of e e−1 ≈ 1.582, which can be derandomized. We 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.

No abstract

We consider the online problem of active queue management. In our model, the input is a sequence of packets with values v ∈ [1, α] that arrive to a queue that can hold up to B packets. Specifically, we consider a FIFO non-preemptive queue, where any packet that is accepted into the queue must be sent, and packets are sent by the order of arrival. The benefit of a scheduling policy, on a given input, is the sum of values of the scheduled packets. Our aim is to find an online policy that maximizes its benefit compared to the optimal offline solution.Previous work proved that no constant competitive ratio exists for this problem, showing a lower bound of ln(α)+1 for any online policy. An upper bound of e ln(α) was proved for a few online policies. In this paper we suggest and analyze a RED-like online policy with a competitive ratio that matches the lower bound up to an additive constant proving an upper bound of ln(α) + 2 + O(ln 2 (α)/B). For large values of α, we prove that no policy whose decisions are based only on the number of packets in the queue and the value of the arriving packet, has a competitive ratio lower than ln(α) + 2 − , for any constant > 0.Submitted to the regular track. Nir Andelman is a full time student at Tel-Aviv University.