com PROCEEDINGS OF THE EIGHTH WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS AND THE THIRD WORKSHOP ON ANALYTIC ALGORITHMICS AND COMBINATORICS CuuDuongThanCong.com SIAM PROCEEDINGS SERIES LIST Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation (2000), Alfredo Bermudez, Dolores Gomez, Christophe Hazard, Patrick Joly, and Jean E Roberts, editors Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms (2001), S Rao Kosaraju, editor Proceedings of the Tenth SIAM Conference on Parallel Processing for Scientific Computing (2001), Charles Koelbel and Juan Meza, editors Computational Information Retrieval (2001), Michael Berry, editor Collected Lectures on the Preservation of Stability under Discretization (2002), Donald Estep and Simon Tavener, editors Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms (2003), Martin FarachColton, editor Proceedings of the Fifth Workshop on Algorithm Engineering and Experiments (2003), Richard E, Ladner, editor Fast Algorithms for Structured Matrices: Theory and Applications (2003), Vadim Olshevsky, editor Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms (2004), Ian Munro, editor Applied Mathematics Entering the 21st Century: Invited Talks from the ICIAM 2003 Congress (2004), James M Hill and Ross Moore, editors Proceedings of the Fourth SIAM International Conference on Data Mining (2004), Michael W Berry, Umeshwar Dayal, Chandrika Kamath, and David Skillicorn, editors Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (2005), Adam Buchsbaum, editor Mathematics for Industry: Challenges and Frontiers A Process View: Practice and Theory (2005), David R Ferguson and Thomas J Peters, editors Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms (2006), Cliff Stein, editor Proceedings of the Eighth Workshop on Algorithm Engineering and Experiments and the Third Workshop on Analytic Algorithmics and Combinatorics (2006), Rajeev Raman, Robert Sedgewick, and Matthias F Stallmann, editors Proceedings of the Sixth SIAM International Conference on Data Mining (2006), Joydeep Ghosh, Diane Lambert, David Skillicorn, and Jaideep Srivastava, editors CuuDuongThanCong.com PROCEEDINGS OF THE EIGHTH WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS AND THE THIRD WORKSHOP ON ANALYTIC ALGORITHMICS AND COMBINATORICS Edited by Rajeev Raman, Robert Sedgewick, and Matthias F Stallmann S1HJTL Society for Industrial and Applied Mathematics Philadelphia CuuDuongThanCong.com PROCEEDINGS OF THE EIGHTH WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS AND THE THIRD WORKSHOP ON ANALYTIC ALGORITHMICS AND COMBINATORICS Proceedings of the Eighth Workshop on Algorithm Engineering and Experiments, Miami, FL, January 21, 2006 Proceedings of the Third Workshop on Analytic Algorithmics and Combinatorics, Miami, FL, January 21, 2006 The workshop was supported by the ACM Special Interest Group on Algorithms and Computation Theory and the Society for Industrial and Applied Mathematics Copyright © 2006 by the Society for Industrial and Applied Mathematics 1098765432 All rights reserved Printed in the United States of America No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher For information, write to the Society for Industrial and Applied Mathematics, 3600 University City Science Center, Philadelphia, PA 19104-2688 Library of Congress Control Number: 2006922417 ISBN 0-89871-610-1 S1HJTL is a registered trademark CuuDuongThanCong.com CONTENTS vii Preface to the Workshop on Algorithm Engineering and Experiments ix Preface to the Workshop on Analytic Algorithmics and Combinatorics Workshop on Algorithm Engineering and Experiments Exact and Efficient Construction of Minkowski Sums of Convex Polyhedra with Applications Efi Fogel and Dan Halperin 16 An Experimental Study of Point Location in General Planar Arrangements Idit Haran and Dan Halperin 26 Summarizing Spatial Data Streams Using ClusterHulls John Hershberger, Nisheeth Shrivastava, and Subhash Suri 41 Distance-Sensitive Bloom Filters Adam Kirsch and Michael Mitzenmacher 51 An Experimental Study of Old and New Depth Measures John Hugg, Eynat Rafalin, Kathryn Seyboth, and Diane Souvaine 65 Keep Your Friends Close and Your Enemies Closer: The Art of Proximity Searching David Mount 66 Implementation and Experiments with an Algorithm for Parallel Scheduling of Complex Dags under Uncertainty Grzegorz Malewicz 75 Using Markov Chains to Design Algorithms for Bounded-Space On-Line Bin Cover Eyjolfur Asgeirsson and Cliff Stein 86 Data Reduction, Exact, and Heuristic Algorithms for Clique Cover Jens Gramm, Jiong Guo, Falk Huffner, and Rolf Niedermeier 95 Fast Reconfiguration of Data Placement in Parallel Disks Srinivas Kashyap, Samir Khuller, Yung-Chun (Justin) Wan, and Leana Golubchik 108 Force-Directed Approaches to Sensor Localization Alon Efrat, David Forrester, Anand Iyer, Stephen G Kobourov, and Cesim Erten 119 Compact Routing on Power Law Graphs with Additive Stretch Arthur Brady and Lenore Cowen 129 Reach for A*: Efficient Point-to-Point Shortest Path Algorithms Andrew V, Goldberg, Haim Kaplan, and Renato F Werneck 144 Distributed Routing in Small-World Networks Oskar Sandberg 156 Engineering Multi-Level Overlay Graphs for Shortest-Path Queries Martin Holzer, Frank Schulz, and Dorothea Wagner 171 Optimal Incremental Sorting Rodrigo Paredes and Gonzalo Navarro v CuuDuongThanCong.com CONTENTS Workshop on Analytic Algorithmics and Combinatorics 185 Deterministic Random Walks Joshua Cooper, Benjamin Doerr, Joel Spencer, and Garbor Tardos 198 Binary Trees, Left and Right Paths, WKB Expansions, and Painleve Transcendents Charles Knessl and Wojciech Szpankowski 205 On the Variance of Quickselect Jean Daligault and Conrado Martinez 211 Semirandom Models as Benchmarks for Coloring Algorithms Michael Krivelevich and Dan Vilenchik 222 New Results and Open Problems for Deletion Channels Michael Mifzenmacher 223 Partial Fillup and Search Time in LC Tries Svante Janson and Wojciech Szpankowski 230 Distinct Values Estimators for Power Law Distributions Rajeev Motwani and Sergei Vassilvitskii 238 A Random-Surfer Web-Graph Model Avrim Blum, T-H Hubert Chan, and Mugizi Robert Rwebangira 247 Asymptotic Optimality of the Static Frequency Caching in the Presence of Correlated Requests Predrag R Jelenkovic and Ana Radovanovic 253 Exploring the Average Values of Boolean Functions via Asymptotics and Experimentation Robin Pemantle and Mark Daniel Ward 263 Permanents of Circulants: A Transfer Matrix Approach Mordecai J Golin, Yiu Cho Leung, and Yajun Wang 273 Random Partitions with Parts in the Range of a Polynomial William M Y Goh and Pawet Hitczenko 281 Author Index VI CuuDuongThanCong.com ALENEX WORKSHOP PREFACE The annual Workshop on Algorithm Engineering and Experiments (ALENEX) provides a forum for the presentation of original research in all aspects of algorithm engineering, including the implementation and experimental evaluation of algorithms and data structures, ALENEX 2006, the eighth workshop in this series, was held in Miami, Florida, on January 21, 2006 The workshop was sponsored by SIAM, the Society for Industrial and Applied Mathematics, and SIGACT, the ACM Special Interest Group on Algorithms and Computation Theory These proceedings contain 15 contributed papers presented at the workshop, together with the abstract of an invited lecture by David Mount, entitled "Keep Your Friends Close and Your Enemies Closer: The Art of Proximity Searching," The contributed papers were selected from a total of 46 submissions based on originality, technical contribution, and relevance Considerable effort was devoted to the evaluation of the submissions with four reviews or more per paper, It is nonetheless expected that most of the papers in these proceedings will eventually appear in finished form in scientific journals The workshop took place on the same day as the Third Workshop on Analytic Algorithmics and Combinatorics (ANALCO 2006), and papers from that workshop also appear in these proceedings As both workshops are concerned with looking beyond the big-oh asymptotic analysis of algorithms, we hope that the ALENEX community will find the ANALCO papers to be of interest We would like to express our gratitude to all the people who contributed to the success of the workshop In particular, we would like thank the authors of submitted papers, the ALENEX Program Committee members, and the external reviewers, Special thanks go to Adam Buchsbaum for answering our many questions along the way, to Andrei Voronkov for timely technical assistance with the use of the EasyChair system, and to Sara Murphy and Sarah M Granlund for coordinating the production of these proceedings Finally, we are indebted to Kirsten Wilden, for all of her valuable help in the many aspects of organizing this workshop Rajeev Raman and Matt Stallmann ALENEX 2006 Program Committee Ricardo Baeza-Yates, UPF, Barcelona, Spain and University of Chile, Santiago Luciana Buriol, University of Rome "La Sapienza," Italy Thomas Erlebach, University of Leicester, United Kingdom Irene Finocchi, University of Rome "La Sapienza," Italy Roberto Grossi, University of Pisa, Italy Lutz Kettner, Max Planck Institute for Informatics, Saarbrucken, Germany Eduardo Sany Laber, PUC, Rio de Janeiro, Brazil Alex Lopez-Ortiz, University of Waterloo, Canada Stefan Naher, University of Trier, Germany Rajeev Raman (co-chair), University of Leicester, United Kingdom Peter Sanders, University of Karlsruhe, Germany Matt Stallmann (co-chair), North Carolina State University lleana Streinu, Smith College Thomas Willhalm, Intel, Germany ALENEX 2006 Steering Committee Lars Arge, University of Aarhus Roberto Battiti, University of Trento Adam Buchsbaum, AT&T Labs—Research Camil Demetrescu, University of Rome "La Sapienza" Andrew V Goldberg, Microsoft Research Michael T Goodrich, University of California, Irvine Giuseppe F Italiano, University of Rome, "Tor Vergata" David S, Johnson, AT&T Labs—Research vii CuuDuongThanCong.com Richard E Ladner, University of Washington Catherine C McGeoch, Amherst College Bernard M.E Moret, University of New Mexico David Mount, University of Maryland, College Park Jack Snoeyink, University of North Carolina, Chapel Hill Clifford Stein, Columbia University Roberto Tamassia, Brown University ALENEX WORKSHOP PREFACE ALENEX 2006 External Reviewers Gad M Landau Marcelo Mas Steffen Mecke Andreas Meyer Ulrich Meyer Gabriel Moruz David Mount Carlos Oliveira Anna Ostlin Pagh Maurizio Patrignani Seth Pettie Derek Phillips Sylvain Pion Maurizio Pizzonia Marcus Poggi Fabio Protti Claude-Guy Quimper Romeo Rizzi Salvator Roura Marie-France Sagot Guido Schaefer Dominik Schultes Frank Schulz Ingolf Sommer Siang Wun Song Renzo Sprugnoli Eduardo Uchoa Ugo Vaccaro Ernst Althaus Spyros Angelopolous Lars Arge Jeremy Barbay Michael Baur Luca Becchetti Iwona Bialynicka-Birula Brona Brejova Saverio Caminiti Timothy Chan Valentina Ciriani Carlos Cotta Roman Dementiev Camil Demetrescu Reza Dorrigiv Mitre Dourado Arash Farzan Gereon Frahling G Franceschini Stefan Funke Marco Gaertler Emilio Di Giacomo Robert Gorke Peter Hachenberger Michael Hoffmann Martin Holzer Daniel Huson Juha Karkkainen Martin Kutz VIII CuuDuongThanCong.com ANALCO WORKSHOP PREFACE The papers in this proceedings, along with an invited talk by Michael Mitzenmacher on "New Results and Open Problems for Deletion Channels," were presented at the Third Workshop on Analytic Algorithmics and Combinatorics (ANALCO06), which was held in Miami on January 21, 2006 The aim of ANALCO is to provide a forum for the presentation of original research in the analysis of algorithms and associated combinatorial structures The papers study properties of fundamental combinatorial structures that arise in practical computational applications (such as permutations, trees, strings, tries, and graphs) and address the precise analysis of algorithms for processing such structures, including average-case analysis; analysis of moments, extrema, and distributions; and probabilistic analysis of randomized algorithms Some of the papers present significant new information about classic algorithms; others present analyses of new algorithms that present unique analytic challenges, or address tools and techniques for the analysis of algorithms and combinatorial structures, both mathematical and computational The workshop took place on the same day as the Eighth Workshop on Algorithm Engineering and Experiments (ALENEX06); the papers from that workshop are also published in this volume Since researchers in both fields are approaching the problem of learning detailed information about the performance of particular algorithms, we expect that interesting synergies will develop, People in the ANALCO community are encouraged to look over the ALENEX papers for problems where the analysis of algorithms might play a role; people in the ALENEX community are encouraged to look over these ANALCO papers for problems where experimentation might play a role ANALCO 2006 Program Committee Jim Fill, Johns Hopkins University Mordecai Golin, Hong Kong University of Science and Technology Philippe Jacquet, INRIA, France Claire Kenyon, Brown University Colin McDiarmid, University of Oxford Daniel Panario, Carleton University Robert Sedgewick (chair), Princeton University Alfredo Viola, University of Uruguay Mark Ward, Purdue University ANALCO 2006 Steering Committee Philippe Flajolet, INRIA, France Robert Sedgewick, Princeton University Wojciech Szpankowski, Purdue University IX CuuDuongThanCong.com LEMMA 2.1 Set and EC (n) is the set of the union of all edges and Then where the union is taken over all such that f(n;u2,V2) — f(n;ui,vi} mod (pn + s) € S Directly from the definition we see Cn is isomorphic to Cn = c^nn++s^p2n+S2'-'pkn+Sk In particular, cyclecovers of Cn are in 1-1 correspondence with cycle covers of Cn so we can restrict ourselves to counting cycle covers of Cn We now introduce the generalization of Definition 2.1 Further set and s = maxs€£- s\ (if S = set s = 0) For later use we define s = s+ + s~ Now define ana DEFINITION 2.3 Let p,s, />1,P2, • ,pk si, s-2, , Sk and 5, / be as in Definition 2.2 Define the pn + s-node lattice graph with jumps S Then where EL(H) is the set of the union of all edges where the union is taken over all Important Note: In this section and the next we will always assume that n>1s since this will guarantee that (L+(n) U L~(n)) n (R+(n) U R~(n)) = Without this such that assumption some of our proofs would fail Also note that the {(n, n)} term in New(n) is only needed when OeS and We now extend the above definitions and lemmas to the case of non-constant circulants This will require a change in the way that we visualize the nodes of Cn\ Now set until, now, as in Figure l(c), we visualized them as points on a line with the edges in Hook(n) connecting and the left and right endpoints of the line In the nonconstant jump case it will be convenient to visualize them as points on a bounded-height lattice, where Note that this implies Hook(n) connects the left and right boundaries of the lattice We start by introducing a new graph: DEFINITION 2.2 See Figure Letp,s, pi,pz, ,pk and s i , S , ,s/e be given integral constants such that V«, < pi < p SetS = {pin+si,p2n+S2,- • • ,Pkn+sk} It is now straightforward to derive an analogue For u, v and integer n, set /(n; w, v) = un + v Define of Lemma 2.1 showing that Hook(?i) and New(n) are independent of the actual value of n Let NV(n) = Vi(n + 1) — VL(JI) NV(n) will be the new vertices in VL(H + 1) Note that we did not define this for fixedwhere jump circulant graphs since in the fixed-jump case there is only the one new vertex V^(n+ 1) — V/,(n) = {n} and NV(n} would be constant 267 CuuDuongThanCong.com LEMMA 2.2 Set IfT is not a legal-cover then we will use the convention that C(T) = Finally, set Then so Tx(n) is the number of legal-covers of Ln with classification X A New Proof of Mine's result Let CC be a cycle-cover of Cn Then, in T = CC — Hook(n), almost all vertices v except possibly those that have an edge of Hook(n) hanging off of them, have H>T(V) = OD r (v) = Referring to (2.4) this motivates DEFINITION 3.1 T C EL(n) is a legal cover of Ln if The main reason for introducing these definitions is that checking whether a legal cover T of Ln can be completed to a cycle-cover of Cn doesn't depend upon all of T but only on its classification C(T) Furthermore, how a legal-cover in Ln expands to a legal cover in Ln+i will also only depend upon C(T) LEMMA 3.2 See Figures and 4(a) LetX = (LX,L*,R%,RX) e P and S C Hook(n) Let T be a legal cover in Ln with C(T] — X Then whether T U S is a cycle cover of Cn depends only upon X and S (and not at all on n) In particular, if T is a legal-cover of Ln and T' is a legal cover of Ln> with C(T] = C(T'} then T U S is a cycle-cover of Cn iff Then, from (2.4) we have Note: We will write X U S is a cycle cover to denote that LEMMA 3.1 (a) IfTC Ec(ri) is a cycle-cover of Cn, then T — Hook(n) is a legal-cover of Ln (b)Let T' be a legal cover in Ln with C(T'} = X' e P and S C New(n) (b) If T C EL(U + 1) is a legal-cover of Ln+i, then Then whether C(T' U S} — X depends only upon T — New(n) is a legal-cover of Ln X' and S (and not at all on n) In particular, ifT' is a legal-cover of Ln and T" is a legal cover of Ln> with From the definition of legal covers we can classify C(T'} = C(T"} then and partition legal covers by the appropriate in/out degrees of their vertices in L+ (ri), L~ (n), R+ (n),R~(n) Note: We will write (X' U S) = X to denote that, when DEFINITION 3.2 A is a binary r-tuple if A - (A(0), A ( l ) , , A(r - 1)) where Vi, A(i) e {0,1} c(r') = x', c(T'us) = x Proof To prove (a) recall that T U S is a legal-cover of Let P be the set of 22s tuples (L+,L_,R+,R_) Ln if and only if, where Z/_|-,L_,.R-|-, R- are, respectively, binary s + , s~, s+, s~ tuples Let T be a legal-cover of Ln The classification of T 268 CuuDuongThanCong.com Figure 3: All of the figures are in C^1'0'2 Dashed edges are Hook(n) The solid plus dashed edges are three different cycle covers CCj, i = 1,2,3 in CQ Removing the dashed Hook(n) edges leaves three legal covers Ti, i = 1, 2, 3, in LQ Note that s+ = and s~ = so classifications are of the form (L+, LT_, R^., R7!} where L+ and RT are pairs and LT_ and R? are singletons Calculation gives C(Ti) = C(T2) = X[ = ((1,0), (0), (0,1), (0)) and C(T3) = X^ = ((0,0), (1), (0,0), (1)) Figure 4: n was increased from to and S — {(4,6)} C New(6) was added to the Tj of the previous figure Note that, in L , C(Ti (J S) = C(T2 U 5) = since they are no longer legal covers Also, C(T3 U 5) = X3(= X^) = ((0,0), (1), (0,0), (1)) Thus, C ( X [ \ J S ) = and CpCg" U S) = X'z From Lemma 2.1 and the definition of a legal cover we LEMMA 3.3 have that this is true if and only if and and this is only dependent upon X and S and not upon n or any other properties of T The proof of (b) is similar and omitted here DEFINITION 3.3 For X,X' e P, S C Hook(n) and S' C New(n) set and Let m = \P\ = 22s Take any arbitrary ordering of P and define the x m constant vector j3 = (flx)x£p and m x m constant matrix A = (ax,x')x,X'£p- Finally, set T(n) = co\(Tx(ri))x£p to be a m x column vector Then, Lemma 3.3 is exactly equation (1.2) which immediately implies that T(n) satisfies a fixeddegree constant coefficient recurrence relation where the degree of the recurrence is at most the degree of any polynomial P(x) such that P(A) — By the Cayley-Hamilton theorem, Q(A) — 0, Q(x) is the degree m = 22s characteristic polynomial Q(x) = det(IX — A) We will now see that it is possible to reduce this degree from 22s down to below 2s LEMMA 3.4 Let A = (ax,xr)- Then there is a degree 2s — polynomial P(x) such that P(A) — Now set Proof Recall that s = s+ + s~ Suppose X = (L*,LX,RX,RX} and X' = (L*',L*',R*', R*') Recall that ax,x' = DscNew(n) 2 Even though these two graphs are not isomorphic they had the same number of cycle-covers because the adjacency matrix of the second is just the adjacency 272 CuuDuongThanCong.com Random partitions with parts in the range of a polynomial5* William M Y Gohf Abstract Let f2(n, Q) be the set of partitions of n into summands that are elements of the set A — {Q(k} : k € Z+} Here Q G Z[x] is a fixed polynomial of degree d > which is increasing on R + , and such that Q(m) is a nonnegative integer for every integer m > For every A G fi(n, Q), let M n (A) be the number of parts, with multiplicity, that A has Put a uniform probability distribution on fi(n, Q), and regard Mn as a random variable The limiting density of the random variable Mn (suitably normalized) is determined explicitly For specific choices of Q, the limiting density has appeared before in rather different contexts such as Kingman's coalescent, and processes associated with the maxima of Brownian bridge and Brownian meander processes Introduction and statement of the result In research on partitions, there have been great synergies between probabilistic, analytic, and combinatorial methods The oldest literature on partition enumerations, dating back to Hardy and Ramanujan [15], has a purely analytic flavor But Erdos and Lehner [11] introduced a probabilistic viewpoint that was quite fruitful Random partitions were developed by Erdos, Szalay, Turan and others, [12, 27, 29, 30, 31, 32] Some authors, e.g [5, 16, 17, 22, 25], have studied random partitions with summands restricted to proper subsets of the set of positive integers Increasingly sophisticated probabilistic ideas have been introduced [13, 2], and these ideas have led to remarkably strong theorems about the joint distribution of part sizes of random integer partitions [23] In this abstract we concentrate on the limiting distribution of the number of parts in a random partition whose parts are restricted to the range of a polynomial Specifically, let Pawel Hitczenko* be a fixed polynomial of degree d > and we assume that Q(x) is strictly increasing for x > and that Q(m) is a non- negative integer for an integer m > Let fj(n, Q} be the set of partitions of n into summands that are elements of the set A = {Q(k) : k £ Z+} For every A fi(n, Q), let M n (A) be the number of parts, with multiplicity, that A has Put a uniform probability measure Pn on fi(n, Q}, and regard Mn as a random variable Note that M n (A) = ]TM a (A), where a Af a (A) is the multiplicity of the part size a in the Pnrandom partition A These random variables Ma are clearly not independent since they must satisfy the condition ]T] aMa = n Fristedt [13] used a conditioning device that enables one to cope with this dependence It quickly proved to be a powerful tool and has been used by several authors in the past decade, see e.g [1, 2, 5, 8, 23, 24, 26] Given a parameter q (0,1), let {Ga} be mutually independent geometric random variables with respective parameters —