6,317 research outputs found
Algorithms as Mechanisms: The Price of Anarchy of Relax-and-Round
Many algorithms that are originally designed without explicitly considering
incentive properties are later combined with simple pricing rules and used as
mechanisms. The resulting mechanisms are often natural and simple to
understand. But how good are these algorithms as mechanisms? Truthful reporting
of valuations is typically not a dominant strategy (certainly not with a
pay-your-bid, first-price rule, but it is likely not a good strategy even with
a critical value, or second-price style rule either). Our goal is to show that
a wide class of approximation algorithms yields this way mechanisms with low
Price of Anarchy.
The seminal result of Lucier and Borodin [SODA 2010] shows that combining a
greedy algorithm that is an -approximation algorithm with a
pay-your-bid payment rule yields a mechanism whose Price of Anarchy is
. In this paper we significantly extend the class of algorithms for
which such a result is available by showing that this close connection between
approximation ratio on the one hand and Price of Anarchy on the other also
holds for the design principle of relaxation and rounding provided that the
relaxation is smooth and the rounding is oblivious.
We demonstrate the far-reaching consequences of our result by showing its
implications for sparse packing integer programs, such as multi-unit auctions
and generalized matching, for the maximum traveling salesman problem, for
combinatorial auctions, and for single source unsplittable flow problems. In
all these problems our approach leads to novel simple, near-optimal mechanisms
whose Price of Anarchy either matches or beats the performance guarantees of
known mechanisms.Comment: Extended abstract appeared in Proc. of 16th ACM Conference on
Economics and Computation (EC'15
Stochastic Vehicle Routing with Recourse
We study the classic Vehicle Routing Problem in the setting of stochastic
optimization with recourse. StochVRP is a two-stage optimization problem, where
demand is satisfied using two routes: fixed and recourse. The fixed route is
computed using only a demand distribution. Then after observing the demand
instantiations, a recourse route is computed -- but costs here become more
expensive by a factor lambda.
We present an O(log^2 n log(n lambda))-approximation algorithm for this
stochastic routing problem, under arbitrary distributions. The main idea in
this result is relating StochVRP to a special case of submodular orienteering,
called knapsack rank-function orienteering. We also give a better approximation
ratio for knapsack rank-function orienteering than what follows from prior
work. Finally, we provide a Unique Games Conjecture based omega(1) hardness of
approximation for StochVRP, even on star-like metrics on which our algorithm
achieves a logarithmic approximation.Comment: 20 Pages, 1 figure Revision corrects the statement and proof of
Theorem 1.
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