From Primal-Dual to Cost Shares and Back: A Stronger LP Relaxation for the Steiner Forest Problem

Könemann, Jochen; Leonardi, Stefano; Schäfer, Guido; Zwam, Stefan van

doi:10.1007/11523468_75

Cited by 17 publications

(14 citation statements)

References 10 publications

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“…Lower bounds on the budget balance factor that is achievable by a cross-monotonic cost-sharing mechanism were studied in [21,26,27].…”

Section: Cost-sharing Mechanismsmentioning

confidence: 99%

“…Constraint (25) imposes that the total contribution of all players towards a facility p does not exceed its opening cost f (p). Constraint (26) enforces that for every facility p ∈ F the cost share ξ i of player i is at most the connection cost c(i, p) plus the contribution κ ip towards p. Constraint (27) requires that the cost share ξ i of each player i is at most the penalty π(i).…”

Section: Lp Formulationmentioning

confidence: 99%

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Efficient cost-sharing mechanisms for prize-collecting problems

et al. 2014

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We consider the problem of designing efficient mechanisms to share the cost of providing some service to a set of self-interested customers. In this paper, we mainly focus on cost functions that are induced by prize-collecting optimization problems. Such cost functions arise naturally whenever customers can be served in two different ways: either by being part of a common service solution or by being served individually.One of our main contributions is a general lifting technique that allows us to extend the social cost approximation guarantee of a Moulin mechanism for A preliminary version of this paper appeared under the title "An efficient cost-sharing mechanism for the prize-collecting Steiner forest problem" in the Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. A. Gupta, J. Könemann, S. Leonardi, R. Ravi and G. Schäfer the respective non-prize-collecting problem to its prize-collecting counterpart. Our lifting technique also suggests a generic design template to derive Moulin mechanisms for prize-collecting problems. The approach is particularly suited for cost-sharing methods that are based on primal-dual algorithms.We illustrate the applicability of our approach by deriving Moulin mechanisms for prize-collecting variants of submodular cost-sharing, facility location and Steiner forest problems. All our mechanisms are essentially best possible with respect to budget balance and social cost approximation guarantees.Finally, we show that the Moulin mechanism by Könemann et al.[27] for the Steiner forest problem is O(log 3 k)-approximate. Our approach adds a novel methodological contribution to existing techniques by showing that such a result can be proved by embedding the graph distances into random hierarchically separated trees.

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“…Lower bounds on the budget balance factor that is achievable by a cross-monotonic cost-sharing mechanism were studied in [21,26,27].…”

Section: Cost-sharing Mechanismsmentioning

confidence: 99%

Section: Lp Formulationmentioning

confidence: 99%

Efficient cost-sharing mechanisms for prize-collecting problems

et al. 2014

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“…This work has given game-theoretic variants of problems like fixed-tree multicast [AFK + 04, FKSS03, FPS01], submodular cost-sharing [MS01], Steiner trees [JV01,KSK96], facility location [PT03], single-source rentor-buy network design [PT03,LS04,GST04], and Steiner forests [KLS05]. Lower bounds on the budget balance achievable by cross-monotonic cost shares are given in [IMM05,KLSvZ05].…”

Section: Contributions Our Main Results Is the Followingmentioning

confidence: 99%

Pricing Tree Access Networks with Connected Backbones

Goyal

Gupta

Leonard

et al. 2007

Algorithms – ESA 2007

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Consider the following network subscription pricing problem. We are given a graph G = (V, E) with a root r, and potential customers are companies headquartered at r with locations at a subset of nodes. Every customer requires a network connecting its locations to r. The network provider can build this network with a combination of backbone edges (consisting of high capacity cables) that can route any subset of the customers, and access edges that can route only a single customer's traffic. The backbone edges cost M times that of the access edges. Our goal is to devise a group-strategyproof pricing mechanism for the network provider, i.e., one in which truth-telling is the optimal strategy for the customers, even in the presence of coalitions. We give a pricing mechanism that is 2-competitive and O(1)-budget-balanced.As a means to obtaining this pricing mechanism, we present the first primal-dual 8-approximation algorithm for this problem. Since the two-stage Stochastic Steiner tree problem can be reduced to the underlying network design, we get a primal-dual algorithm for the stochastic problem as well. Finally, as a byproduct of our techniques, we also provide bounds on the inefficiency of our mechanism.

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“…Note, that it suffices to consider the optimal cost instead of the LPT cost in Eq. (25). If an α-fraction of the optimal cost cannot be recovered, in particular it cannot be recovered for a non-optimal cost.…”

Section: Cross-monotonicitymentioning

confidence: 97%

“…Remarkably, most known group-strategyproof mechanisms for non-submodular cost functions nevertheless rely on cross-monotonic cost-sharing methods and use a simple mechanism given by Moulin [27] that guarantees groupstrategyproofness. Cross-monotonic cost-sharing methods have been suggested for TSP, Minimal Spanning Tree, and Steiner Tree [22,23], Steiner Forest [24,25], Facility Location [9,26,29], Multi-Commodity-Rent-or-Buy [6], Single-Source-Rent-or-Buy [18,29], Set Cover [9], and Multicast [2,10,11]. Only the methods for Minimal Spanning Trees achieve budget-balance.…”

mentioning

confidence: 99%

Fair cost-sharing methods for scheduling jobs on parallel machines

Bleischwitz

Monien

2009

Journal of Discrete Algorithms

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a r t i c l e i n f o a b s t r a c tWe consider the problem of sharing the cost of scheduling n jobs on m parallel machines among a set of agents. In our setting, each agent owns exactly one job and the cost is given by the makespan of the computed assignment. We focus on α-budget-balanced crossmonotonic cost-sharing methods since they guarantee the two substantial mechanism properties α-budget-balance and group-strategyproofness and provide fair cost-shares. For identical jobs on related machines and for arbitrary jobs on identical machines, we give (m + 1)/(2m)-budget-balanced cross-monotonic cost-sharing methods and show that this is the best approximation possible. As our major result, we prove that the approximation factor for cross-monotonic cost-sharing methods is unbounded for arbitrary jobs and related machines. We therefore develop a cost-sharing method in the (m + 1)/(2m)-core, a weaker but also fair solution concept.

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From Primal-Dual to Cost Shares and Back: A Stronger LP Relaxation for the Steiner Forest Problem

Cited by 17 publications

References 10 publications

Efficient cost-sharing mechanisms for prize-collecting problems

Efficient cost-sharing mechanisms for prize-collecting problems

Pricing Tree Access Networks with Connected Backbones

Fair cost-sharing methods for scheduling jobs on parallel machines

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