2,947 research outputs found
Non-Atomic One-Round Walks in Polynomial Congestion Games
Abstract. In this paper we study the approximation ratio of the solutions achieved after an -approximate one-round walk in non-atomic congestion games. Prior to this work, the solution concept of one-round walks had been studied for atomic congestion games with linear latency functions onl
On the Impact of Singleton Strategies in Congestion Games
To what extent does the structure of the players\u27 strategy space influence the efficiency of decentralized solutions in congestion games? In this work, we investigate whether better performance is possible when restricting to load balancing games in which players can only choose among single resources. We consider three different solutions concepts, namely, approximate pure Nash equilibria, approximate one-round walks generated by selfish players aiming at minimizing their personal cost and approximate one-round walks generated by cooperative players aiming at minimizing the marginal increase in the sum of the players\u27 personal costs. The last two concepts can also be interpreted as solutions of simple greedy online algorithms for the related resource selection problem. Under fairly general latency functions on the resources, we show that, for all three types of solutions, better bounds cannot be achieved if players are either weighted or asymmetric. On the positive side, we prove that, under mild assumptions on the latency functions, improvements on the performance of approximate pure Nash equilibria are possible for load balancing games with weighted and symmetric players in the case of identical resources. We also design lower bounds on the performance of one-round walks in load balancing games with unweighted players and identical resources (in this case, solutions generated by selfish and cooperative players coincide)
Nash Social Welfare in Selfish and Online Load Balancing (Short Paper)
In load balancing problems there is a set of clients, each wishing to select a resource from a set of permissible ones, in order to execute a certain task. Each resource has a latency function, which depends on its workload, and a client's cost is the completion time of her chosen resource. Two fundamental variants of load balancing problems are selfish load balancing (aka. load balancing games), where clients are non-cooperative selfish players aimed at minimizing their own cost solely, and online load balancing, where clients appear online and have to be irrevocably assigned to a resource without any knowledge about future requests. We revisit both problems under the objective of minimizing the Nash Social Welfare, i.e., the geometric mean of the clients' costs. To the best of our knowledge, despite being a celebrated welfare estimator in many social contexts, the Nash Social Welfare has not been considered so far as a benchmarking quality measure in load balancing problems. We provide tight bounds on the price of anarchy of pure Nash equilibria and on the competitive ratio of the greedy algorithm under very general latency functions, including polynomial ones. For this particular class, we also prove that the greedy strategy is optimal, as it matches the performance of any possible online algorithm
A Cut-Matching Game for Constant-Hop Expanders
This paper provides a cut-strategy that produces constant-hop expanders in
the well-known cut-matching game framework.
Constant-hop expanders strengthen expanders with constant conductance by
guaranteeing that any demand can be (obliviously) routed along constant-hop
paths - in contrast to the -hop routes in expanders.
Cut-matching games for expanders are key tools for obtaining
close-to-linear-time approximation algorithms for many hard problems, including
finding (balanced or approximately-largest) sparse cuts, certifying the
expansion of a graph by embedding an (explicit) expander, as well as computing
expander decompositions, hierarchical cut decompositions, oblivious routings,
multi-cuts, and multicommodity flows. The cut-matching game provided in this
paper is crucial in extending this versatile and powerful machinery to
constant-hop expanders. It is also a key ingredient towards close-to-linear
time algorithms for computing a constant approximation of multicommodity-flows
and multi-cuts - the approximation factor being a constant relies on the
expanders being constant-hop
Optimized network structure and routing metric in wireless multihop ad hoc communication
Inspired by the Statistical Physics of complex networks, wireless multihop ad
hoc communication networks are considered in abstracted form. Since such
engineered networks are able to modify their structure via topology control, we
search for optimized network structures, which maximize the end-to-end
throughput performance. A modified version of betweenness centrality is
introduced and shown to be very relevant for the respective modeling. The
calculated optimized network structures lead to a significant increase of the
end-to-end throughput. The discussion of the resulting structural properties
reveals that it will be almost impossible to construct these optimized
topologies in a technologically efficient distributive manner. However, the
modified betweenness centrality also allows to propose a new routing metric for
the end-to-end communication traffic. This approach leads to an even larger
increase of throughput capacity and is easily implementable in a
technologically relevant manner.Comment: 25 pages, v2: fixed one small typo in the 'authors' fiel
Improving Approximate Pure Nash Equilibria in Congestion Games
Congestion games constitute an important class of games to model resource
allocation by different users. As computing an exact or even an approximate
pure Nash equilibrium is in general PLS-complete, Caragiannis et al. (2011)
present a polynomial-time algorithm that computes a ()-approximate pure Nash equilibria for games with linear cost
functions and further results for polynomial cost functions. We show that this
factor can be improved to and further improved results for
polynomial cost functions, by a seemingly simple modification to their
algorithm by allowing for the cost functions used during the best response
dynamics be different from the overall objective function. Interestingly, our
modification to the algorithm also extends to efficiently computing improved
approximate pure Nash equilibria in games with arbitrary non-decreasing
resource cost functions. Additionally, our analysis exhibits an interesting
method to optimally compute universal load dependent taxes and using linear
programming duality prove tight bounds on PoA under universal taxation, e.g,
2.012 for linear congestion games and further results for polynomial cost
functions. Although our approach yield weaker results than that in Bil\`{o} and
Vinci (2016), we remark that our cost functions are locally computable and in
contrast to Bil\`{o} and Vinci (2016) are independent of the actual instance of
the game
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