Aaron Archer

Truthful mechanisms for one-parameter agents

The authors show how to design truthful (dominant strategy) mechanisms for several combinatorial problems where each agents secret data is naturally expressed by a single positive real number. The goal of the mechanisms we consider is to allocate loads placed on the agents, and an agents secret data is the cost she incurs per unit load. We give an exact characterization for the algorithms that can be used to design truthful mechanisms for such load balancing problems using appropriate side payments. We use our characterization to design polynomial time truthful mechanisms for several problems in combinatorial optimization to which the celebrated VCG mechanism does not apply. For scheduling related parallel machines (Q/spl par/C/sub max/), we give a 3-approximation mechanism based on randomized rounding of the optimal fractional solution. This problem is NP-complete, and the standard approximation algorithms (greedy load-balancing or the PTAS) cannot be used in truthful mechanisms. We show our mechanism to be frugal, in that the total payment needed is only a logarithmic factor more than the actual costs incurred by the machines, unless one machine dominates the total processing power. We also give truthful mechanisms for maximum flow, Q/spl par//spl Sigma/C/sub j/ (scheduling related machines to minimize the sum of completion times), optimizing an affine function over a fixed set, and special cases of uncapacitated facility location. In addition, for Q/spl par//spl Sigma/w/sub j/C/sub j/ (minimizing the weighted sum of completion times), we prove a lower bound of 2//spl radic/3 for the best approximation ratio achievable by truthful mechanism.

Frugal path mechanisms

We consider the problem of selecting a low cost s --- t path in a graph, where the edge costs are a secret known only to the various economic agents who own them. To solve this problem, Nisan and Ronen applied the celebrated Vickrey-Clarke-Groves (VCG) mechanism, which pays a premium to induce edges to reveal their costs truthfully. We observe that this premium can be unacceptably high. There are simple instances where the mechanism pays Θ(k) times the actual cost of the path, even if there is alternate path available that costs only (1 + ε) times as much. This inspires the frugal path problem, which is to design a mechanism that selects a path and induces truthful cost revelation without paying such a high premium.This paper contributes negative results on the frugal path problem. On two large classes of graphs, including ones having three node-disjoint s - t paths, we prove that no reasonable mechanism can always avoid paying a high premium to induce truthtelling. In particular, we introduce a general class of min function mechanisms, and show that all min function mechanisms can be forced to overpay just as badly VCG. On the other hand, we prove that (on two large classes of graphs) every truthful mechanism satisfying some reasonable properties is a min function mechanism.

An Approximate Truthful Mechanism for Combinatorial Auctions with Single Parameter Agents

Mechanism design seeks algorithms whose inputs are provided by selfish agents who would lie if advantageous. Incentive compatible mechanisms compel the agents to tell the truth by making it in their self-interest to do so. Often, as in combinatorial auctions, such mechanisms involve the solution of NP-hard problems. Unfortunately, approximation algorithms typically destroy incentive compatibility. Randomized rounding is a commonly used technique for designing approximation algorithms. We devise a version of randomized rounding that is incentive compatible, giving a truthful mechanism for combinatorial auctions with single parameter agents (e.g., single minded bidders) that approximately maximizes the social value of the auction. We discuss two orthogonal notions of truthfulness for a randomized mechanism, truthfulness with high probability and in expectation, and give a mechanism that achieves both simultaneously.We consider combinatorial auctions where multiple copies of many different items are on sale, and each bidder i desires a subset Si. Given a set of bids, the problem of finding the allocation of items that maximizes total valuation is the well-known SETPACKING problem. This problem is NP-hard, but for the case of items with many identical copies the optimum can be approximated very well. To turn this approximation algorithm into a truthful auction mechanism we overcome two problems: we show how to make the allocation algorithm monotone, and give a method to compute the appropriate payments efficiently.

Approximation and collusion in multicast cost sharing

Abstract We investigate multicast cost sharing from both computational and economic perspectives. Recent work in economics leads to the consideration of two mechanisms: marginal cost (MC), which is efficient and strategyproof, and Shapley value (SH), which is budget-balanced and group-strategyproof. Subsequent work in computer science shows that the MC mechanism can be computed with only two modest-sized messages per link of the multicast tree but that computing the SH mechanism for p potential receivers can require Ω(p) bits of communication per link. We extend these results in two directions. First, we give a group-strategyproof mechanism that exhibits a tradeoff between the other properties of SH: It can be computed with exponentially lower worst-case communication than the SH algorithm, but it might fail to achieve exact budget balance (albeit by a bounded amount). Second, we completely characterize the groups that can strategize successfully against the MC mechanism.

A Faster, Better Approximation Algorithm for the Minimum Latency Problem

We give a 7.18-approximation algorithm for the minimum latency problem that uses only

A Modern Treatment of the 15 Puzzle

O(n log n)

Lagrangian Relaxation for the k-Median Problem: New Insights and Continuity Properties

calls to the prize-collecting Steiner tree (PCST) subroutine of Goemans and Williamson. This improves the previous best algorithms in both performance guarantee and running time. A previous algorithm of Goemans and Kleinberg for the minimum latency problem requires an approximation algorithm for the

Two O (log* k)-Approximation Algorithms for the Asymmetric k-Center Problem

k

On the upper chromatic numbers of the reals

-minimum spanning tree (

An approximate truthful mechanism for combinatorial auctions with single parameter agents

k