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221
Balanced Allocations
 SIAM Journal on Computing
, 1994
"... Suppose that we sequentially place n balls into n boxes by putting each ball into a randomly chosen box. It is well known that when we are done, the fullest box has with high probability (1 + o(1)) ln n/ ln ln n balls in it. Suppose instead that for each ball we choose two boxes at random and place ..."
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Cited by 331 (8 self)
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Suppose that we sequentially place n balls into n boxes by putting each ball into a randomly chosen box. It is well known that when we are done, the fullest box has with high probability (1 + o(1)) ln n/ ln ln n balls in it. Suppose instead that for each ball we choose two boxes at random and place the ball into the one which is less full at the time of placement. We show that with high probability, the fullest box contains only ln ln n/ ln 2 +O(1) balls  exponentially less than before. Furthermore, we show that a similar gap exists in the infinite process, where at each step one ball, chosen uniformly at random, is deleted, and one ball is added in the manner above. We discuss consequences of this and related theorems for dynamic resource allocation, hashing, and online load balancing.
An Overview of QualityofService Routing for the Next Generation HighSpeed Networks: Problems and Solutions
"... The upcoming Gbps highspeed networks are expected to support a wide range of communicationintensive, realtime multimedia applications. The requirement for timely delivery of digitized audiovisual information raises new challenges for the next generation integratedservice broadband networks. On ..."
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Cited by 223 (22 self)
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The upcoming Gbps highspeed networks are expected to support a wide range of communicationintensive, realtime multimedia applications. The requirement for timely delivery of digitized audiovisual information raises new challenges for the next generation integratedservice broadband networks. One of the key issues is the QualityofService (QoS) routing. It selects network routes with sufficient resources for the requested QoS parameters. The goal of routing solutions is twofold: (1) satisfying the QoS requirements for every admitted connection and (2) achieving the global efficiency in resource utilization. Many unicast/multicast QoS routing algorithms were published recently, and they work with a variety of QoS requirements and resource constraints. Overall, they can be partitioned into three broad classes: (1) source routing, (2) distributed routing and (3) hierarchical routing algorithms. In this paper we give an overview of the QoS routing problem as well as the existing solutions. We present the strengths and the weaknesses of different routing strategies and outline the challenges. We also discuss the basic algorithms in each class, classify and compare them, and point out possible future directions in the QoS routing area.
Approximation Algorithms for Disjoint Paths Problems
, 1996
"... The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems for w ..."
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Cited by 166 (0 self)
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The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems for which very little is known from the point of view of approximation algorithms. It has recently been brought into focus in work on problems such as VLSI layout and routing in highspeed networks; in these settings, the current lack of understanding of the disjoint paths problem is often an obstacle to the design of practical heuristics.
Efficient routing in alloptical networks
 in Proc. 26 th ACM Symp. Theory of Computing
, 1994
"... Communication in alloptical networks requires novel routing paradigms. The high bandwidth of the optic fiber is utilized through wavelengthdivision multiplexing: a single physical optical link can carry several logical signals, provided that they are transmitted on different wavelengths. We study t ..."
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Cited by 123 (0 self)
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Communication in alloptical networks requires novel routing paradigms. The high bandwidth of the optic fiber is utilized through wavelengthdivision multiplexing: a single physical optical link can carry several logical signals, provided that they are transmitted on different wavelengths. We study the problem of routing a set of requests (each of which is a pair of nodes to be connected by a path) on sparse networks using a limited number of wavelengths, ensuring that different paths using the same wavelength never use the same physical link. The constraints on the selection of paths and wavelengths depend on the type of photonic switches used in the network. We present eflicient routing techniques for the two types of photonic switches that dominate current research in alloptical networks. Our results es
Incentive compatible multi unit combinatorial auctions
 In TARK 03
, 2003
"... This paper deals with multiunit combinatorial auctions where there are n types of goods for sale, and for each good there is some fixed number of units. We focus on the case where each bidder desires a relatively small number of units of each good. In particular, this includes the case where each g ..."
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Cited by 113 (13 self)
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This paper deals with multiunit combinatorial auctions where there are n types of goods for sale, and for each good there is some fixed number of units. We focus on the case where each bidder desires a relatively small number of units of each good. In particular, this includes the case where each good has exactly k units, and each bidder desires no more than a single unit of each good. We provide incentive compatible mechanisms for combinatorial auctions for the general case where bidders are not limited to single minded valuations. The mechanisms we give have approximation ratios close to the best possible for both online and offline scenarios. This is the first result where nonVCG mechanisms are derived for nonsingle minded bidders for a natural model of combinatorial auctions.
Competitive NonPreemptive Call Control
"... We deal with randomized competitive algorithms for nonpreemptive call control on treelike switching networks. We give an optimal O(log n) competitive algorithm for nonpreemptive call scheduling on trees. We then extend the problem to include variable call rates, call durations, and arbitrary call ..."
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Cited by 107 (8 self)
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We deal with randomized competitive algorithms for nonpreemptive call control on treelike switching networks. We give an optimal O(log n) competitive algorithm for nonpreemptive call scheduling on trees. We then extend the problem to include variable call rates, call durations, and arbitrary call benefits, and obtain a polylog competitive algorithm. We also show that many similar algorithms for different problems that can deal with constant values of parameters such as rates and benefits can be transformed into randomized algorithms that can deal with varying values of the parameters.
Competitive Routing of Virtual Circuits in ATM networks
 IEEE Journal on Selected Areas in Communications
"... Classical routing and admission control strategies achieve provably good performance by relying on an assumption that the virtual circuits arrival pattern can be described by some a priori known probabilistic model. Recently a new online routing framework, based on the notion of competitive analysis ..."
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Cited by 94 (0 self)
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Classical routing and admission control strategies achieve provably good performance by relying on an assumption that the virtual circuits arrival pattern can be described by some a priori known probabilistic model. Recently a new online routing framework, based on the notion of competitive analysis, was proposed. This framework is geared towards design of strategies that have provably good performance even in the case where there are no statistical assumptions on the arrival pattern and parameters of the virtual circuits. The online strategies motivated by this framework are quite different from the minhop and reservationbased strategies. This paper surveys the online routing framework, the proposed routing and admission control strategies, and discusses some of the implementation issues. Research supported by NSF CCR9304971, ARO DAAH049510121, and by Terman Fellowship. EMail: plotkin@cs.stanford.edu, URL: http://theory.stanford.edu/people/plotkin/plotkin.html. 1 Introducti...
Approximation Techniques for Utilitarian Mechanism Design
, 2005
"... This paper deals with the design of efficiently computable incentive compatible, or truthful, mechanisms for combinatorial optimization problems with multiparameter agents. We focus on approximation algorithms for NPhard mechanism design problems. These algorithms need to satisfy certain monotonic ..."
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Cited by 93 (5 self)
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This paper deals with the design of efficiently computable incentive compatible, or truthful, mechanisms for combinatorial optimization problems with multiparameter agents. We focus on approximation algorithms for NPhard mechanism design problems. These algorithms need to satisfy certain monotonicity properties to ensure truthfulness. Since most of the known approximation techniques do not fulfill these properties, we study alternative techniques. Our first contribution is a quite general method to transform a pseudopolynomial algorithm into a monotone FPTAS. This can be applied to various problems like, e.g., knapsack, constrained shortest path, or job scheduling with deadlines. For example, the monotone FPTAS for the knapsack problem gives a very efficient, truthful mechanism for singleminded multiunit auctions. The best previous result for such auctions was a 2approximation. In addition, we present a monotone PTAS for the generalized assignment problem with any bounded number of parameters per agent. The most efficient way to solve packing integer programs (PIPs) is LPbased randomized rounding, which also is in general not monotone. We show that primaldual greedy algorithms achieve almost the same approximation ratios for PIPs as randomized rounding. The advantage is that these algorithms are inherently monotone. This way, we can significantly improve the approximation ratios of truthful mechanisms for various fundamental mechanism design problems like singleminded combinatorial auctions (CAs), unsplittable flow routing and multicast routing. Our approximation algorithms can also be used for the winner determination in CAs with general bidders specifying their bids through an oracle.
OnLine Routing of Virtual Circuits with Applications to Load Balancing and Machine Scheduling
, 1993
"... In this paper we study the problem of online allocation of routes to virtual circuits (both pointtopoint and multicast) where the goal is to minimize the required bandwidth. We concentrate on the case of permanent virtual circuits (i.e., once a circuit is established, it exists forever), and descr ..."
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Cited by 87 (4 self)
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In this paper we study the problem of online allocation of routes to virtual circuits (both pointtopoint and multicast) where the goal is to minimize the required bandwidth. We concentrate on the case of permanent virtual circuits (i.e., once a circuit is established, it exists forever), and describe an algorithm that achieves an O(log n) competitive ratio with respect to maximum congestion, where n is the number of nodes in the network. Informally, our results show that instead of knowing all of the future requests, it is sufficient to increase the bandwidth of the communication links by an O(log n) factor. We also show that this result is tight, i.e. for any online algorithm there exists a scenario in which O(log n) increase in bandwidth is necessary. We view virtual circuit routing as a generalization of an online load balancing problem, defined as follows: jobs arrive on line and each job must be assigned to one of the machines immediately upon arrival. Assigning a job to a machine increases this machine’s load by an amount that depends both on the job and on the machine. The goal is to minimize the maximum load. For the related machines case, we describe the first algorithm that achieves constant competitive ratio. For the unrelated case (with n machines), we describe a new method that yields O(log n)competitive
High Throughput Route Selection in MultiRate Ad Hoc Wireless Networks
, 2003
"... An ad hoc wireless network is an autonomous self organizing system of mobile nodes connected by wireless links where nodes not in direct range communicate via intermediate nodes. Modern wireless devices, such as those that implement the 802.11b standard, utilize multiple transmission rates in order ..."
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Cited by 86 (3 self)
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An ad hoc wireless network is an autonomous self organizing system of mobile nodes connected by wireless links where nodes not in direct range communicate via intermediate nodes. Modern wireless devices, such as those that implement the 802.11b standard, utilize multiple transmission rates in order to accommodate a wide range of channel conditions. We provide a general theoretical model of the attainable throughput in multi rate ad hoc wireless networks. This model is derived from a de tailed analysis of the physical and medium access control layers.