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A Theoretician's Guide to the Experimental Analysis of Algorithms
, 1996
"... This paper presents an informal discussion of issues that arise when one attempts to analyze algorithms experimentally. It is based on lessons learned by the author over the course of more than a decade of experimentation, survey paper writing, refereeing, and lively discussions with other experimen ..."
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Cited by 77 (0 self)
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This paper presents an informal discussion of issues that arise when one attempts to analyze algorithms experimentally. It is based on lessons learned by the author over the course of more than a decade of experimentation, survey paper writing, refereeing, and lively discussions with other experimentalists. Although written from the perspective of a theoretical computer scientist, it is intended to be of use to researchers from all fields who want to study algorithms experimentally. It has two goals: first, to provide a useful guide to new experimentalists about how such work can best be performed and written up, and second, to challenge current researchers to think about whether their own work might be improved from a scientific point of view. With the latter purpose in mind, the author hopes that at least a few of his recommendations will be considered controversial.
Vmalloc: A General and Efficient Memory Allocator
, 1996
"... Introduction Dynamic memory allocation is an integral part of programming. Programs in C and C++ (via constructors and destructors) routinely allocate memory using the familiar ANSIC standard interface malloc established around 1979 by Doug McIlroy. Malloc manipulates heap memory using the functi ..."
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Cited by 47 (7 self)
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Introduction Dynamic memory allocation is an integral part of programming. Programs in C and C++ (via constructors and destructors) routinely allocate memory using the familiar ANSIC standard interface malloc established around 1979 by Doug McIlroy. Malloc manipulates heap memory using the functions malloc(s) to allocate a block of size s, free(b) to free a previously allocated block b, and realloc(b,s) to resize a block b to size s. No optimal solution to dynamic memory allocation exists [1, 2, 3] so, over the years, many malloc implementations were proposed with different tradeoffs in time and space efficiency. A study by David Korn and Phong Vo in 1985 presented and compared 11 malloc versions. Only a few of these survived the test of time. The first widely used malloc was written by McIlroy and became part of many Bell Labs Research and System V versions of the UNIX system. This malloc is based on a firstfit strategy and can be significantly slow in large memories. C. King
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.
Bin Packing with Discrete Item Sizes Part II: AverageCase Behavior of FFD and BFD
 In preparation
, 1997
"... This is for the abstract page Bin Packing with Discrete Item Sizes Part II: AverageCase Behavior of FFD and BFD E. G. Coffman, Jr. and D. S. Johnson AT&T Bell Laboratories Murray Hill, NJ 07974 L. A. McGeoch Amherst College Amherst, MA 01002 R. R. Weber Cambridge University Cambridge UK 1. ..."
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Cited by 20 (5 self)
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This is for the abstract page Bin Packing with Discrete Item Sizes Part II: AverageCase Behavior of FFD and BFD E. G. Coffman, Jr. and D. S. Johnson AT&T Bell Laboratories Murray Hill, NJ 07974 L. A. McGeoch Amherst College Amherst, MA 01002 R. R. Weber Cambridge University Cambridge UK 1. Introduction Consider the bin packing problem in which a list L n of n items, with sizes drawn from the unit interval, is to be partitioned into a smallest collection of blocks such that, for each block, the sum of the sizes of the items in the block is at most 1. With applications in mind, a partitioning algorithm solving this problem is said to pack the items of L n into a minimum number of unitcapacity bins. The problem is NPhard, so a great deal of effort has gone into the analysis of efficient approximation algorithms. The analysis of primary interest here is probabilistic, or averagecase analysis (see [5] for a recent book on the subject). This paper analyzes the expected behavior...
WaferScale Integration of Systolic Arrays
 IEEE Transactions on Computers
, 1985
"... AbstractVLSI technologists are fast developing waferscale integration. Rather than partitioning a silicon wafer into chips as is usually done, the idea behind waferscale integration is to assemble an entire system (or network of chips) on a single wafer, thus avoiding the costs and performance lo ..."
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Cited by 17 (0 self)
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AbstractVLSI technologists are fast developing waferscale integration. Rather than partitioning a silicon wafer into chips as is usually done, the idea behind waferscale integration is to assemble an entire system (or network of chips) on a single wafer, thus avoiding the costs and performance loss associated with individual packaging of chips. A major problem with assembling a large system of microprocessors on a single wafer, however, is that some of the processors, or cells, on the wafer are likely to be defective. In the paper, we describe practical procedures for integrating "around " such faults. The procedures are designed to minimize the length of the longest wire in the system, thus minimizing the communication time between cells. Although the underlying network problems are NPcomplete, we prove that the procedures are reliable by assuming a probabilistic model of cell failure. We also discuss applications of the work to problems in VLSI layout theory, graph theory, faulttolerant systems, planar geometry, and the probabilistic analysis of algorithms. Index Terms Channel width, faulttolerant systems, matching, probabilistic analysis, spanning tree, systolic arrays, traveling salesman problem, tree of meshes, VLSI, waferscale integration, wire length. I.
Bounded Space OnLine Bin Packing: Best is Better than First
 In Proc. 2nd ACMSIAM Symp. Discrete Algorithms, 309319
, 1991
"... We present a sequence of new lineartime, boundedspace, online bin packing algorithms, the KBounded Best Fit algorithms (BBF K ). They are based on the Q(nlogn) Best Fit algorithm in much the same way as the NextK Fit algorithms are based on the Q(nlogn) First Fit algorithm. Unlike the NextK Fi ..."
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Cited by 9 (1 self)
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We present a sequence of new lineartime, boundedspace, online bin packing algorithms, the KBounded Best Fit algorithms (BBF K ). They are based on the Q(nlogn) Best Fit algorithm in much the same way as the NextK Fit algorithms are based on the Q(nlogn) First Fit algorithm. Unlike the NextK Fit algorithms, whose asymptotic worstcase ratios approach the limiting value of 17/10 from above as K ® but never reach it, these new algorithms have worstcase ratio 17/10 for all K ³ 2. They also have substantially better average performance than their boundedspace competition, as we have determined based on extensive experimental results summarized here for instances with item sizes drawn independently and uniformly from intervals of the form (0 , u], 0 < u 1. Indeed, for each u < 1, it appears that there exists a fixed memory bound K(u) such that BBF K(u) obtains significantly better packings on average than does the First Fit algorithm, even though the latter requires unbounded storag...
Perfect Packing Theorems and the AverageCase Behavior of Optimal and Online Bin Packing
 SIAM Review
, 2002
"... We consider the onedimensional bin packing problem under the discrete uniform distributions U{j, k}, 1 1, in which the bin capacity is k and item sizes are chosen uniformly from the set 2, . . . , j}. Note that for 0 < u = j/k 1 this is a discrete version of the previously studied con ..."
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Cited by 6 (1 self)
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We consider the onedimensional bin packing problem under the discrete uniform distributions U{j, k}, 1 1, in which the bin capacity is k and item sizes are chosen uniformly from the set 2, . . . , j}. Note that for 0 < u = j/k 1 this is a discrete version of the previously studied continuous uniform distribution U(0, u], where the bin capacity is 1 and item sizes are chosen uniformly from the interval (0, u]. We show that the averagecase performance of heuristics can di#er substantially between the two types of distributions. In particular, there is an online algorithm that has constant expected wasted space under U{j, k} for any j, k with 1 1, whereas no online algorithm can have o(n ) expected waste under U(0, u] for any 0 < u 1. Our U{j, k} result is an application of a general theorem of Courcoubetis and Weber that covers all discrete distributions. Under each such distribution, the optimal expected waste for a random list of n items must be either #(n), #(n ), or O(1), depending on whether certain "perfect" packings exist. The perfect packing theorem needed for the U{j, k} distributions is an intriguing result of independent combinatorial interest, and its proof is a cornerstone of the paper. We also survey other recent results comparing the behavior of heuristics under discrete and continuous uniform distributions.
Linear Waste of Best Fit Bin Packing on Skewed Distributions
 in Proceedings of the 41st Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA
, 2000
"... We prove that Best Fit bin packing has linear waste on the discrete distribution U{j, k} (where items are drawn uniformly from the set 2/k, , j/k}) for sufficiently large k when j = #k and 0.66 # < 2/3. Our results extend to continuous skewed distributions, where items are drawn uniform ..."
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Cited by 6 (1 self)
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We prove that Best Fit bin packing has linear waste on the discrete distribution U{j, k} (where items are drawn uniformly from the set 2/k, , j/k}) for sufficiently large k when j = #k and 0.66 # < 2/3. Our results extend to continuous skewed distributions, where items are drawn uniformly on [0, a], for 0.66 a < 2/3. This implies that the expected asymptotic performance ratio of Best Fit is strictly greater than 1 for these distributions.
Bin Packing with Queues ∗
, 2006
"... We study the best achievable performance (in terms of average queue size and delay) in a stochastic and dynamic version of the binpacking problem. Items arrive to a queue according to a Poisson process with rate 2ρ, where ρ ∈ (0, 1). The item sizes are i.i.d., uniformly distributed in [0, 1]. At ea ..."
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Cited by 2 (2 self)
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We study the best achievable performance (in terms of average queue size and delay) in a stochastic and dynamic version of the binpacking problem. Items arrive to a queue according to a Poisson process with rate 2ρ, where ρ ∈ (0, 1). The item sizes are i.i.d., uniformly distributed in [0, 1]. At each time unit, a single unitsize bin is available and can receive any of the queued items, as long as their total size does not exceed one. Coffman & Stolyar (1999) and Gamarnik (2001) have established that there exist packing policies under which the average queue size is finite, for every ρ ∈ (0, 1). In this paper, we study the precise scaling of the average queue size, as a function of ρ, with emphasis on the critical regime where ρ approaches one. Standard results on the probabilistic (but static) binpacking problem can be readily applied to produce policies under which the queue size scales as O(h 2), where h = 1/(1 − ρ), which raises the question whether this is the best possible. We establish that the average queuesize scales as Ω(h log h), under any policy. Furthermore, we provide an easily implementable policy, which packs at most two items per bin. Under that policy, the average queue size scales as O(h log 3/2 h), which is nearly optimal. On the other hand, if we impose the additional requirement that any two items packed together must have nearcomplementary sizes (in a sense to be made precise), we show that the average queue size must scale as Θ(h 2). Keywords: Binpacking, queueing, heavy traffic.
Stochastic Bandwidth Packing Process: Stability Conditions via Lyapunov Function Technique
, 2004
"... Abstract. We consider the following stochastic bandwidth packing process: the requests for communica14 14 tion bandwidth of different sizes arrive at times t = 0, 1, 2,...and are allocated to a communication link 15 using “largest first ” rule. Each request takes a unit time to complete. The unallo ..."
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Cited by 1 (0 self)
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Abstract. We consider the following stochastic bandwidth packing process: the requests for communica14 14 tion bandwidth of different sizes arrive at times t = 0, 1, 2,...and are allocated to a communication link 15 using “largest first ” rule. Each request takes a unit time to complete. The unallocated requests form queues. 15 16 Coffman and Stolyar [6] introduced this system and posed the following question: under which conditions 16 17 do the expected queue lengths remain bounded over time (queueing system is stable)? We derive exact 17 18 constructive conditions for the stability of this system using the Lyapunov function technique. The result 18 holds under fairly general assumptions on the distribution of the arrival processes. 19 19 20 Keywords: bin packing, queueing networks, positive recurrence