We study single-candidate voting embedded in a metric space, where both voters and candidates are points in the space, and the distances between voters and candidates specify the voters' preferences over candidates. In the voting, each voter is asked to submit her favorite candidate. Given the collection of favorite candidates, a mechanism for eliminating the least popular candidate finds a committee containing all candidates but the one to be eliminated. Each committee is associated with a social value that is the sum of the costs (utilities) it imposes (provides) to the voters. We design mechanisms for finding a committee to optimize the social value. We measure the quality of a mechanism by its distortion, defined as the worst-case ratio between the social value of the committee found by the mechanism and the optimal one. We establish new upper and lower bounds on the distortion of mechanisms in this single-candidate voting, for both general metrics and well-motivated special cases.

This work concerns the mechanism design for online scheduling in a strategic setting. In this setting, each job is owned by a self-interested agent who may misreport the release time, deadline, length, and value of her job, while we need to determine not only the schedule of the jobs, but also the payment of each agent. We focus on the design of incentive compatible (IC) mechanisms, and study the maximization of social welfare (i.e., the aggregated value of completed jobs) by competitive analysis. We first derive two lower bounds on the competitive ratio of any deterministic IC mechanism to characterize the landscape of our research: one bound is 5, which holds for equal-length jobs; the other bound is $\frac{\kappa}{\ln\kappa}+1-o(1)$, which holds for unequal-length jobs, where $\kappa$ is the maximum ratio between lengths of any two jobs. We then propose a deterministic IC mechanism and show that such a simple mechanism works very well for two models: (1) In the preemption-restart model, the mechanism can achieve the optimal competitive ratio of 5 for equal-length jobs and a near optimal ratio of $(\frac{1}{(1-\epsilon)^2}+o(1)) \frac{\kappa}{\ln\kappa}$ for unequal-length jobs, where $0<\epsilon<1$ is a small constant; (2) In the preemption-resume model, the mechanism can achieve the optimal competitive ratio of 5 for equal-length jobs and a near optimal competitive ratio (within factor 2) for unequal-length jobs.

Selfish routing is one of the fundamental models in the study of network traffic systems. While most literature assumes essentially static flows, game theoretical models of dynamic flows began to draw attention recently [1, 5].

This paper concerns the mechanism design for online scheduling in a strategic setting. In this setting, each job is owned by a self-interested agent who may misreport the release time, deadline, length, and value of her job, while we need to determine not only the schedule of the jobs, but also the payment of each agent. We focus on the design of incentive compatible (IC) mechanisms, and study the maximization of social welfare (i.e., the aggregated value of completed jobs) by competitive analysis. We first derive two lower bounds on the competitive ratio of any deterministic IC mechanism to characterize the landscape of our research. We then propose a deterministic IC mechanism and show that such a simple mechanism works very well for both the preemption-restart model and the preemption-resume model. We show the mechanism can achieve the optimal competitive ratio of 5 for equal-length jobs and a near optimal competitive ratio (within a constant factor) for unequal-length jobs.

Facility location, arising in a rich variety of applications, has been studied extensively in the fields of operations research and computer science. In this paper we consider the classical uncapacitated facility location problem and its “prize-collecting" variant introduced by Baïou and Barahona, and we show that the linear systems associated with these problems are totally dual integral if and only if the input graphs do not contain a certain type of odd cycles. As corollaries, we get structural characterizations of two min-max relations on facility location. Our results strengthen the integrality theorems on facility location polytopes proved by Baïou and Barahona; our proofs lead to combinatorial polynomial-time algorithms for the facility location problems that we consider.

Given a preference system $(G, \prec)$ and an integral weight function defined on the edge set of $G$ (not necessarily bipartite), the maximum-weight stable matching problem is to find a stable matching of $(G, \prec)$ with maximum total weight. In this paper we study this $NP$-hard problem using linear programming and polyhedral approaches. We show that the Rothblum system for defining the fractional stable matching polytope of $(G, \prec)$ is totally dual integral if and only if this polytope is integral if and only if $(G, \prec)$ has a bipartite representation. We also present a combinatorial polynomial-time algorithm for the maximum-weight stable matching problem and its dual on any preference system with a bipartite representation. Our results generalize Király and Pap's theorem on the maximum-weight stable-marriage problem and rely heavily on their work.

Abstract This article is concerned with the design of fault‐tolerant access networks for cost‐effective communications—deploying network links and service providers (SPs) at a minimum cost, while ensuring error tolerance ability via the ring architecture. Given a set of service subscribers (SSs) in an access network, we are required to determine the locations and capacities of service providers, and to establish network links in terms of rings connecting SSs to SPs. We pay link costs for ring constructions and pay management costs for selecting SPs with capacities sufficient to manage the SSs in their rings. The network design aims to minimize the sum of the link costs and the management costs. Two APX‐hard problems in the general network design are studied in this article to address the scalable and modular features of SP capacities. Despite the logarithmic inapproximability that we show for one problem, constant‐factor approximation algorithms are proposed to solve the other problem and its variant in quartic time. © 2009 Wiley Periodicals, Inc. NETWORKS, 2009

We present a structural characterization of all tournaments $T=(V,A)$ such that, for any nonnegative integral weight function defined on V, the maximum size of a feedback vertex set packing is equal to the minimum weight of a triangle in T. We also answer a question of Frank by showing that it is $NP$-complete to decide whether the vertex set of a given tournament can be partitioned into two feedback vertex sets. In addition, we give exact and approximation algorithms for the feedback vertex set packing problem on tournaments.