40,453 research outputs found
Lower Bounds for the Fair Resource Allocation Problem
The -fair resource allocation problem has received remarkable
attention and has been studied in numerous application fields. Several
algorithms have been proposed in the context of -fair resource sharing
to distributively compute its value. However, little work has been done on its
structural properties. In this work, we present a lower bound for the optimal
solution of the weighted -fair resource allocation problem and compare
it with existing propositions in the literature. Our derivations rely on a
localization property verified by optimization problems with separable
objective that permit one to better exploit their local structures. We give a
local version of the well-known midpoint domination axiom used to axiomatically
build the Nash Bargaining Solution (or proportionally fair resource allocation
problem). Moreover, we show how our lower bound can improve the performances of
a distributed algorithm based on the Alternating Directions Method of
Multipliers (ADMM). The evaluation of the algorithm shows that our lower bound
can considerably reduce its convergence time up to two orders of magnitude
compared to when the bound is not used at all or is simply looser.Comment: in IFIP WG 7.3 Performance 2017, New York, NY US
Lower Bounds for the Fair Resource Allocation Problem
International audienceThe α-fair resource allocation problem has received remarkable attention and has been studied in numerous application fields. Several algorithms have been proposed in the context of α-fair resource sharing to distributively compute its value. However, little work has been done on its structural properties. In this work, we present a lower bound for the optimal solution of the weighted α-fair resource allocation problem and compare it with existing propositions in the literature. Our derivations rely on a localization property verified by optimization problems with separable objective that permit one to better exploit their local structures. We give a local version of the well-known midpoint domination axiom used to axiomatically build the Nash Bargaining Solution (or proportionally fair resource allocation problem). Moreover, we show how our lower bound can improve the performances of a distributed algorithm based on the Alternating Directions Method of Multipliers (ADMM). The evaluation of the algorithm shows that our lower bound can considerably reduce its convergence time up to two orders of magnitude compared to when the bound is not used at all or is simply looser
Resource allocations with guaranteed awards in claims problems
The notion of lower bound on awards has been introduced in the literature to analyze the establishment of guarantees that ensure a minimum award to each agent involved in situations of conflicting claims, such as the rationing of a resource or the distribution of the assets of a bankrupt firm. Indeed, this concept has a core role in many approaches related to the problem of fair allocation (Thomson in Math Soc Sci 74:41–59, 2015) and a range of such lower bounds have been proposed: the minimal right (Curiel et al. in Z Oper Res 31:A143–A159, 1987), the fair bound (Moulin in Handb Soc Choice Welf 1:289–357, 2002), securement (Moreno-Ternero and Villar in Math Soc Sci 47(2):245–257, 2004) and the min bound (Dominguez in mimeo, 2006). In this context, the key contribution of the current paper is to show that there is a correspondence between lower bounds and rules; i.e., associated to each particular lower bound, we find a specific way of distributing the resources. In doing so, we provide new characterizations for two well known rules, the constrained equal awards and Ibn Ezra’s rules. A dual analysis, by using upper bounds on awards will provide characterizations of the dual of the previously mentioned rules: the constrained equal losses rule and the dual of Ibn Ezra’s rule.Open access funding provided by Universitat Rovira i Virgili. Financial support from Universitat Rovira i Virgili and Generalitat de Catalunya (2018PFR-URV-B2-53) and Ministerio de EconomÃa y Competitividad (ECO2016-75410-P (AEI/FEDER, UE), ECO2017-86481-P (AEI/ FEDER, UE) and PID2020-119152GB-I00 (AEI/FEDER, UE)) is acknowledged
Routing Games with Progressive Filling
Max-min fairness (MMF) is a widely known approach to a fair allocation of
bandwidth to each of the users in a network. This allocation can be computed by
uniformly raising the bandwidths of all users without violating capacity
constraints. We consider an extension of these allocations by raising the
bandwidth with arbitrary and not necessarily uniform time-depending velocities
(allocation rates). These allocations are used in a game-theoretic context for
routing choices, which we formalize in progressive filling games (PFGs).
We present a variety of results for equilibria in PFGs. We show that these
games possess pure Nash and strong equilibria. While computation in general is
NP-hard, there are polynomial-time algorithms for prominent classes of
Max-Min-Fair Games (MMFG), including the case when all users have the same
source-destination pair. We characterize prices of anarchy and stability for
pure Nash and strong equilibria in PFGs and MMFGs when players have different
or the same source-destination pairs. In addition, we show that when a designer
can adjust allocation rates, it is possible to design games with optimal strong
equilibria. Some initial results on polynomial-time algorithms in this
direction are also derived
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