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52
On the SumofSquares algorithms for bin packing
, 2006
"... In this article we present a theoretical analysis of the online SumofSquares algorithm (SS) for bin packing along with several new variants. SS is applicable to any instance of bin packing in which the bin capacity B and item sizes s(a) are integral (or can be scaled to be so), and runs in time ..."
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Cited by 108 (7 self)
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In this article we present a theoretical analysis of the online SumofSquares algorithm (SS) for bin packing along with several new variants. SS is applicable to any instance of bin packing in which the bin capacity B and item sizes s(a) are integral (or can be scaled to be so), and runs in time O(nB). It performs remarkably well from an average case point of view: For any discrete distribution in which the optimal expected waste is sublinear, SS also has sublinear expected waste. For any discrete distribution where the optimal expected waste is bounded, SS has expected waste at most O(log n). We also discuss several interesting variants on SS, including a randomized O(nBlog B)time online algorithm SS ∗ whose expected behavior is essentially optimal for all discrete distributions. Algorithm SS ∗ depends on a new linearprogrammingbased pseudopolynomialtime algorithm for solving the
Adversarial Queuing Theory
, 2001
"... We consider packet routing when packets are injected continuously into a network. We develop an adversarial theory of queuing aimed at addressing some of the restrictions inherent in probabilistic analysis and queuing theory based on timeinvariant stochastic generation. We examine the stability of ..."
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Cited by 75 (0 self)
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We consider packet routing when packets are injected continuously into a network. We develop an adversarial theory of queuing aimed at addressing some of the restrictions inherent in probabilistic analysis and queuing theory based on timeinvariant stochastic generation. We examine the stability of queuing networks and policies when the arrival process is adversarial, and provide some preliminary results in this direction. Our approach sheds light on various queuing policies in simple networks, and paves the way for a systematic study of queuing with few or no probabilistic assumptions.
Evolutionary Algorithms and the Maximum Matching Problem
, 2002
"... Randomized search heuristics like evolutionary algorithms are mostly applied to problems whose structure is not completely known but also to combinatorial optimization problems. Practitioners report surprising successes but almost no results with theoretically wellfounded analyses exist. Such a ..."
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Cited by 65 (10 self)
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Randomized search heuristics like evolutionary algorithms are mostly applied to problems whose structure is not completely known but also to combinatorial optimization problems. Practitioners report surprising successes but almost no results with theoretically wellfounded analyses exist. Such an analysis is started in this paper for a fundamental evolutionary algorithm and the wellknown maximum matching problem. It is
Protocols and impossibility results for gossipbased communication mechanisms
, 2002
"... In recent years, gossipbased algorithms have gained prominence as a methodology for designing robust and scalable communication schemes in large distributed systems. The premise underlying distributed gossip is very simple: in each time step, each node v in the system selects some other node w as a ..."
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Cited by 55 (3 self)
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In recent years, gossipbased algorithms have gained prominence as a methodology for designing robust and scalable communication schemes in large distributed systems. The premise underlying distributed gossip is very simple: in each time step, each node v in the system selects some other node w as a communication partner — generally by a simple randomized rule — and exchanges information with w; over a period of time, information spreads through the system in an “epidemic fashion”. A fundamental issue which is not well understood is the following: how does the underlying lowlevel gossip mechanism — the means by which communication partners are chosen — affect one’s ability to design efficient highlevel gossipbased protocols? We establish one of the first concrete results addressing this question, by showing a fundamental limitation on the power of the commonly used uniform gossip mechanism for solving nearestresource location problems. In contrast, very efficient protocols for this problem can be designed using a nonuniform spatial gossip mechanism, as established in earlier work with Alan Demers. We go on to consider the design of protocols for more complex problems, providing an efficient distributed gossipbased protocol for a set of nodes in Euclidean space to construct an approximate minimum spanning tree. Here too, we establish a contrasting limitation on the power of uniform gossip for solving this problem. Finally, we investigate gossipbased packet routing as a primitive that underpins the communication patterns in many protocols, and as a way to understand the capabilities of different gossip mechanisms at a general level.
UniversalStability Results and Performance Bounds for Greedy ContentionResolution Protocols
"... In this paper, we analyze the behavior of packetswitched communication networks in which packets arrive dynamically at the nodes and are routed in discrete time steps across the edges. We focus on a basic adversarial model of packet arrival and path determination for which the timeaveraged arriva ..."
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Cited by 33 (2 self)
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In this paper, we analyze the behavior of packetswitched communication networks in which packets arrive dynamically at the nodes and are routed in discrete time steps across the edges. We focus on a basic adversarial model of packet arrival and path determination for which the timeaveraged arrival rate of packets requiring the use of any edge is limited to be less than 1. This model can reflect the behavior of connectionoriented networks with transient connections (such as ATM networks) as well as connectionless networks (such as the Internet). We concentrate on
Greedy Dynamic Routing on Arrays
 Proceedings of the Sixth Annual ACMSIAM Symposium on Discrete Algorithms
, 1995
"... We study the problem of dynamic routing on arrays. We prove that a large class of greedy algorithms perform very well on average. In the dynamic case, when the arrival rate of packets in an N \Theta N array is at most 99% of network capacity, we establish an exponential bound on the tail of the dela ..."
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Cited by 23 (4 self)
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We study the problem of dynamic routing on arrays. We prove that a large class of greedy algorithms perform very well on average. In the dynamic case, when the arrival rate of packets in an N \Theta N array is at most 99% of network capacity, we establish an exponential bound on the tail of the delay distribution. Moreover, we show that, in any window of T steps, the maximum queuesize is O(1 + log T= log N ) with high probability. We extend these results to the case of bitserial routing, and to the static case. We also calculate the exact value of the ergodic expected delay and queuesizes under the farthestfirst protocol for the one dimensional array, and for the ring when the arrivals are Poisson. 1 Introduction Many parallel machines, such as the MPP, Ametek and Intel Touchstone are configured as a lowdimensional array containing a large number of processors. These machines generally route packets using simple greedy algorithms. While these algorithms tend to behave well experi...
Biased Random Walks, Lyapunov Functions, and Stochastic Analysis of Best Fit Bin Packing
, 1995
"... We study the Best Fit algorithm for online bin packing under the distribution in which the item sizes are uniformly distributed in the discrete range f1=k � 2=k�:::�j=kg. Our main result is that, in the case j = k; 2, the asymptotic expected waste remains bounded. This settles an open problem of Co ..."
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Cited by 22 (6 self)
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We study the Best Fit algorithm for online bin packing under the distribution in which the item sizes are uniformly distributed in the discrete range f1=k � 2=k�:::�j=kg. Our main result is that, in the case j = k; 2, the asymptotic expected waste remains bounded. This settles an open problem of Co man et al [3], and involves a detailed analysis of the in nite multidimensional Markov chain underlying the algorithm.
On The Effect of Populations in Evolutionary Multiobjective Optimization
"... Abstract. Multiobjective evolutionary algorithms (MOEAs) have become increasingly popular as multiobjective problem solving techniques. Most studies of MOEAs are empirical. Only recently, a few theoretical results have appeared. It is acknowledged that more theoretical research is needed. An impor ..."
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Cited by 18 (3 self)
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Abstract. Multiobjective evolutionary algorithms (MOEAs) have become increasingly popular as multiobjective problem solving techniques. Most studies of MOEAs are empirical. Only recently, a few theoretical results have appeared. It is acknowledged that more theoretical research is needed. An important open problem is to understand the role of populations in MOEAs. We present a simple biobjective problem which emphasizes when populations are needed. Rigorous runtime analysis point out an exponential runtime gap between a populationbased algorithm (SEMO) and several single individualbased algorithms on this problem. This means that among the algorithms considered, only the populationbased MOEA is successful and all other algorithms fail. 1
On the Optimization of Monotone Polynomials by Simple Randomized Search Heuristics
, 2002
"... Randomized search heuristics like evolutionary algorithms and simulated annealing find many applications, especially in situations where no full information on the problem instance is available. In order to understand how these heuristics work, it is necessary to analyze their behavior on classe ..."
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Cited by 16 (10 self)
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Randomized search heuristics like evolutionary algorithms and simulated annealing find many applications, especially in situations where no full information on the problem instance is available. In order to understand how these heuristics work, it is necessary to analyze their behavior on classes of functions. Such an analysis is performed here for the class of monotone pseudoboolean polynomials. Results depending on the degree and the number of terms of the polynomial are obtained. The class of monotone polynomials is of special interest since simple functions of this kind can have an image set of exponential size, improvements can increase the Hamming distance to the optimum and in order to find a better search point, it can be necessary to search within a large plateau of search points with the same fitness value.
Randomized communication in radio networks
 HANDBOOK OF RANDOMIZED COMPUTING
, 2001
"... A communication network is called a radio network if its nodes exchange messages in the following restricted way. First, a send operation performed by a node delivers copies of the same message to all directly reachable nodes. Secondly, a node can successfully receive an incoming message only if exa ..."
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Cited by 14 (0 self)
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A communication network is called a radio network if its nodes exchange messages in the following restricted way. First, a send operation performed by a node delivers copies of the same message to all directly reachable nodes. Secondly, a node can successfully receive an incoming message only if exactly one of its neighbors sent a message in that step. It is this semantics of how ports at nodes send and receive messages that defines the networks rather than the fact that only radio waves are used as a medium of communication; but if that is the case then just a single frequency is used. We discuss algorithmic aspects of exchanging information in such networks, concentrating on distributed randomized protocols. Specific problems and solutions depend a lot on the topology of the underlying reachability graph and how much the nodes know about it. In singlehop networks each pair of nodes can communicate directly. This kind of networks is also known as the multiple access channel. Popular