1,430 research outputs found
Optimal Oblivious Routing in Polynomial Time
A recent seminal result of Räcke is that for any network there is an oblivious routing algorithm with a polylog competitive ratio with respect to congestion. Unfortunately, Räcke's construction is not polynomial time. We give a polynomial time construction that guarantee's Räcke's bounds, and more generally gives the true optimal ratio for any network
Compact Oblivious Routing
Oblivious routing is an attractive paradigm for large distributed systems in which centralized control and frequent reconfigurations are infeasible or undesired (e.g., costly). Over the last almost 20 years, much progress has been made in devising oblivious routing schemes that guarantee close to optimal load and also algorithms for constructing such schemes efficiently have been designed. However, a common drawback of existing oblivious routing schemes is that they are not compact: they require large routing tables (of polynomial size), which does not scale.
This paper presents the first oblivious routing scheme which guarantees close to optimal load and is compact at the same time - requiring routing tables of polylogarithmic size. Our algorithm maintains the polylogarithmic competitive ratio of existing algorithms, and is hence particularly well-suited for emerging large-scale networks
Optimal oblivious routing under linear and ellipsoidal uncertainty
In telecommunication networks, a common measure is the maximum congestion (i.e., utilization) on edge capacity. As traffic demands are often known with a degree of uncertainty, network management techniques must take into account traffic variability. The oblivious performance of a routing is a measure of how congested the network may get, in the worst case, for one of a set of possible traffic demands. We present two models to compute, in polynomial time, the optimal oblivious routing: a linear model to deal with demands bounded by box constraints, and a second-order conic program to deal with ellipsoidal uncertainty, i.e., when a mean-variance description of the traffic demand is given. A comparison between the optimal oblivious routing and the well-known OSPF routing technique on a set of real-world networks shows that, for different levels of uncertainty, optimal oblivious routing has a substantially better performance than OSPF routing. © Springer Science+Business Media, LLC 2007
A note on hierarchical hubbing for a generalization of the VPN problem
Robust network design refers to a class of optimization problems that occur
when designing networks to efficiently handle variable demands. The notion of
"hierarchical hubbing" was introduced (in the narrow context of a specific
robust network design question), by Olver and Shepherd [2010]. Hierarchical
hubbing allows for routings with a multiplicity of "hubs" which are connected
to the terminals and to each other in a treelike fashion. Recently, Fr\'echette
et al. [2013] explored this notion much more generally, focusing on its
applicability to an extension of the well-studied hose model that allows for
upper bounds on individual point-to-point demands. In this paper, we consider
hierarchical hubbing in the context of a previously studied (and extremely
natural) generalization of the hose model, and prove that the optimal
hierarchical hubbing solution can be found efficiently. This result is relevant
to a recently proposed generalization of the "VPN Conjecture".Comment: 14 pages, 1 figur
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
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