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265
Approximating the minimumdegree Steiner tree to within one of optimal
 JOURNAL OF ALGORITHMS
, 1994
"... ... some optimal tree for the respective problems. Unless P = N P, this is the best bound achievable in polynomial time. ..."
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Cited by 84 (4 self)
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... some optimal tree for the respective problems. Unless P = N P, this is the best bound achievable in polynomial time.
AuctionBased MultiRobot Routing
, 2005
"... Recently auction methods have been investigated as effective, decentralized methods for multirobot coordination. Experimental research has shown great potential, but has not been complemented yet by theoretical analysis. In this paper we contribute a theoretical analysis of the performance of auc ..."
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Cited by 84 (11 self)
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Recently auction methods have been investigated as effective, decentralized methods for multirobot coordination. Experimental research has shown great potential, but has not been complemented yet by theoretical analysis. In this paper we contribute a theoretical analysis of the performance of auction methods for multirobot routing. We suggest a generic framework for auctionbased multirobot routing and analyze a variety of bidding rules for different team objectives. This is the first time that auction methods are shown to offer theoretical guarantees for such a variety of bidding rules and team objectives.
Scheduling Algorithms
, 1997
"... Introduction Scheduling theory is concerned with the optimal allocation of scarce resources to activities over time. The practice of this field dates to the first time two humans contended for a shared resource and developed a plan to share it without bloodshed. The theory of the design of algorith ..."
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Cited by 79 (1 self)
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Introduction Scheduling theory is concerned with the optimal allocation of scarce resources to activities over time. The practice of this field dates to the first time two humans contended for a shared resource and developed a plan to share it without bloodshed. The theory of the design of algorithms for scheduling is younger, but still has a significant historythe earliest papers in the field were published more than forty years ago. Scheduling problems arise in a variety of settings, as is illustrated by the following examples: Example 1: Consider the central processing unit of a computer that must process a sequence of jobs that arrive over time. In what order should the jobs be processed in order to minimize, on average, the time that a job is in the system from arrival to completion? Example 2: Consider a team of five astronauts preparing for the reentry of their space shuttle into the at
Fairness in routing and load balancing
 J. Comput. Syst. Sci
, 1999
"... We consider the issue of network routing subject to explicit fairness conditions. The optimization of fairness criteria interacts in a complex fashion with the optimization of network utilization and throughput; in this work, we undertake an investigation of this relationship through the framework o ..."
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Cited by 74 (0 self)
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We consider the issue of network routing subject to explicit fairness conditions. The optimization of fairness criteria interacts in a complex fashion with the optimization of network utilization and throughput; in this work, we undertake an investigation of this relationship through the framework of approximation algorithms. In a range of settings including both highspeed networks and Internet applications, maxmin fairness has emerged as a widely accepted formulation of the notion of fairness. Informally, we say that an allocation of bandwidth is maxmin fair if there is no way to give more bandwidth to any connection without decreasing the allocation to a connection of lesser or equal bandwidth. Given a collection of transmission routes, this criterion imposes a certain equilibrium condition on the bandwidth allocation, and some simple flow control mechanisms converge quickly to this equilibrium state. Indeed, the vast majority of previous work on maxmin fairness has focused on this issue of associating rates with connections that are specified by a fixed set of paths. Very little work has been devoted to understanding the relationship between the way in which one selects paths
Selfish Load Balancing and Atomic Congestion Games
, 2007
"... We revisit a classical load balancing problem in the modern context of decentralized systems and selfinterested clients. In particular, there is a set of clients, each of whom must choose a server from a permissible set. Each client has a unitlength job and selfishly wants to minimize its own late ..."
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Cited by 72 (3 self)
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We revisit a classical load balancing problem in the modern context of decentralized systems and selfinterested clients. In particular, there is a set of clients, each of whom must choose a server from a permissible set. Each client has a unitlength job and selfishly wants to minimize its own latency (job completion time). A server’s latency is inversely proportional to its speed, but it grows linearly with (or, more generally, as the pth power of) the number of clients matched to it. This interaction is naturally modeled as an atomic congestion game, which we call selfish load balancing. We analyze the Nash equilibria of this game and prove nearly tight bounds on the price of anarchy (worstcase ratio between a Nash solution and the social optimum). In particular, for linear latency functions, we show that if the server speeds are relatively bounded and the number of clients is large compared with the number of servers, then every Nash assignment approaches social optimum. Without any assumptions on the number of clients, servers, and server speeds, the price of anarchy is at most 2.5. If all servers have the same speed, then the price of anarchy further improves to 1 + 2 / √ 3 ≈ 2.15. We also exhibit a lower bound of 2.01. Our proof techniques can also be adapted for the coordinated load balancing problem under L2 norm, where it slightly improves the best previously known upper bound on the competitive ratio of a simple greedy scheme.
On approximately fair allocations of indivisible goods
 In ACM Conference on Electronic Commerce (EC
, 2004
"... We study the problem of fairly allocating a set of indivisible goods to a set of people from an algorithmic perspective. Fair division has been a central topic in the economic literature and several concepts of fairness have been suggested. The criterion that we focus on is the maximum envy between ..."
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We study the problem of fairly allocating a set of indivisible goods to a set of people from an algorithmic perspective. Fair division has been a central topic in the economic literature and several concepts of fairness have been suggested. The criterion that we focus on is the maximum envy between any pair of players. An allocation is called envyfree if every player prefers her own share than the share of any other player. When the goods are divisible or when there is sufficient amount of one divisible good, envyfree allocations always exist. In the presence of indivisibilities however this is not the case. We first show that when all goods are indivisible, there always exist allocations in which the envy is bounded by the maximum marginal utility and we present a simple polynomial time algorithm for computing such allocations. We further show that our algorithm can be applied to the continuous cakecutting model as well and obtain a procedure that produces ɛenvyfree allocations with a linear number of cuts. We then look at the optimization problem of finding an allocation with minimum possible envy. In the general case, there is no polynomial time algorithm (or even approximation algorithm) for the problem, unless P = NP. We consider natural special cases (e.g. additive utilities) which are closely related to a class of job scheduling problems. Polynomial time approximation algorithms as well as inapproximability results are obtained. Finally we investigate the problem of designing truthful mechanisms for producing allocations with bounded envy. 1
Dependent rounding and its applications to approximation algorithms
 JOURNAL OF THE ACM
, 2006
"... We develop a new randomized rounding approach for fractional vectors defined on the edgesets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to improved (approximation) algorithms for various problems. These include: ffl low congestion multipath rout ..."
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Cited by 61 (8 self)
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We develop a new randomized rounding approach for fractional vectors defined on the edgesets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to improved (approximation) algorithms for various problems. These include: ffl low congestion multipath routing; ffl richer randomgraph models for graphs with a given degreesequence; ffl improved approximation algorithms for: (i) throughputmaximization in broadcast scheduling, (ii) delayminimization in broadcast scheduling, as well as (iii) capacitated vertex cover; and
SingleSource Unsplittable Flow
 In Proceedings of the 37th Annual Symposium on Foundations of Computer Science
, 1996
"... The maxflow mincut theorem of Ford and Fulkerson is based on an even more foundational result, namely Menger's theorem on graph connectivity. Menger's theorem provides a good characterization for the following singlesource disjoint paths problem: given a graph G, with a source vertex s ..."
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Cited by 60 (2 self)
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The maxflow mincut theorem of Ford and Fulkerson is based on an even more foundational result, namely Menger's theorem on graph connectivity. Menger's theorem provides a good characterization for the following singlesource disjoint paths problem: given a graph G, with a source vertex s and terminals t 1 , ..., t k , decide whether there exist edgedisjoint st i paths, for i = 1, ..., k. We consider a natural, NPhard generalization of this problem, which we call the singlesource unsplittable flow problem. We are given a source and terminals as before; but now each terminal t i has a demand ae i 1, and each edge e of G has a capacity c e 1. The problem is to decide whether one can choose a single st i path, for each i, so that the resulting set of paths respects the capacity constraints  the total amount of demand routed across any edge e must be bounded by the capacity c e . The main results of this paper are constantfactor approximation algorithms for three n...
An Approximation Algorithm for MaxMin Fair Allocation of Indivisible goods
 In Proc. of the ACM Symposium on Theory of Computing (STOC
"... In this paper, we give the first approximation algorithm for the problem of maxmin fair allocation of indivisible goods. An instance of this problem consists of a set of k people and m indivisible goods. Each person has a known linear utility function over the set of goods which might be different ..."
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Cited by 59 (2 self)
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In this paper, we give the first approximation algorithm for the problem of maxmin fair allocation of indivisible goods. An instance of this problem consists of a set of k people and m indivisible goods. Each person has a known linear utility function over the set of goods which might be different from the others’. The goal is to distribute the goods among the people and maximize the minimum utility received by them. 1 The approximation ratio of our algorithm is Ω ( √ k log3). As a crucial part of our k algorithm, we design and analyze an iterative method for rounding a fractional matching on a tree which might be of independent interest. We also provide better bounds when we are allowed to exclude a small fraction of the people from the problem.
Coordination mechanisms
 PROCEEDINGS OF THE 31ST INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING, IN: LECTURE NOTES IN COMPUTER SCIENCE
, 2004
"... We introduce the notion of coordination mechanisms to improve the performance in systems with independent selfish and noncolluding agents. The quality of a coordination mechanism is measured by its price of anarchy—the worstcase performance of a Nash equilibrium over the (centrally controlled) soc ..."
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Cited by 57 (5 self)
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We introduce the notion of coordination mechanisms to improve the performance in systems with independent selfish and noncolluding agents. The quality of a coordination mechanism is measured by its price of anarchy—the worstcase performance of a Nash equilibrium over the (centrally controlled) social optimum. We give upper and lower bounds for the price of anarchy for selfish task allocation and congestion games.