Algorithm Theory — SWAT'96: 5th Scandinavian Workshop on Algorithm Theory Reykjavík, Iceland, July 3–5, 1996 Proceedings

461 Pages·1996·7.17 MB·English

by  Noga Alon (auth.)

Lecture Notes in Computer Science 1097
Edited by G. Goos, J. Hartmanis and J. van Leeuwen
Advisory Board: .W Brauer D. Gries J. Stoer
RolfKarlsson Andrzej Lingas ).sdE(
mhtiroglA yroehT
TAWS '96
Workshop 5th Scandinavian
Algorithm Theory on
Reykjavik, Iceland, July 3-5, 6991
Proceedings
regnirpS
Series Editors
Gerhard Goos, Karlsruhe University, Germany
Juris Hartmanis, Cornell University, NY, USA
Jan van Leeuwen, Utrecht University, The Netherlands
Volume Editors
Rolf Karlsson
Andrzej Lingas
Lund University, Department of Computer Science
P.O. Box 118, S-22100 Lund, Sweden
Cataloging-in-Publication data applied for
Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Algorithm theory : proceedings / SWAT '96, 5th Scandinavian
Workshop on Algorithm Theory, Reykjavik, Iceland, July 3 - 5,
1996. Rolf Karlsson ; Andrzej Lingas (ed.). - Berlin ;
Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kong ;
London ; Milan ; Paris ; Santa Clara ; Singapore ; Tokyo :
Springer, 1996
(Lecture notes in computer science ; Vol. 1097)
ISBN 3-540-61422-2
NE: Karlsson, Rolf Hrsg.; SWAT <5, 1996, Reykjavik>; GT
CR Subject Classification (1991): F:l-2, E.1-2, G.2, G.3, 1.3.5
ISSN 0302-9743
ISBN 3-540-61422-2 Springer-Verlag Berlin Heidelberg New York
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Foreword
The papers in this volume were presented at the Fifth Scandinavian Work-
shop on Algorithm Theory. The workshop, which continues the tradi-
tion of SWAT'88 to SWAT'94, and of the Workshops on Algorithms and
Data Structures .(WADS'89 to WADS'95), is intended as a forum for re-
searchers in the area of design and analysis of algorithms. The SWAT con-
ferences are coordinated by the SWAT steering committee, which consists of
B. Aspvall (Bergen), S. Carlsson (Lule£), H. Hafsteinsson (Reykjav~k),
R. Karlsson (Lund), A. Lingas (Lund), E.M. Schmidt (/~rhus), and
E. Ukkonen (Helsinki).
The call for papers sought contributions on original research on algo-
rithms and data structures, in all areas, including computational geometry,
parallel and distributed computing, graph theory, and combinatorics. There
were 95 papers submitted, of which about two thirds were very good or good.
Because of the SWAT format the program committee could select only 35
papers for presentation. In addition, invited lectures were presented by Noga
Alon (Tel-Aviv), Arne Andersson (Lund), and Mike Paterson (Warwick).
SWAT'96 was held on July 3-5, 1996, in Reykjav~k, Iceland, and was or-
ganized by Hj£1mt:~r Hafsteinsson and Magnds Hallddrsson (University of
Iceland).
We wish to thank all referees who helped to evaluate the papers. We are
grateful to Nordic Research Courses (NorFA), the Ministry of Education of
Iceland, the city of Reykjav[k, Lund University, and the Swedish Research
Council for Engineering Sciences (TFR) for their support.
Lund, April 1996 Rolf Karlsson
Andrzej Lingas
Table of Contents
Derandomization Via Small Sample Spaces (Invited Lecture)
N. Alon ............................................................. 1
The Randomized Complexity of Maintaining the Minimum
G.S. Brodal, S. Chaudhuri, J. Radhakrishnan ....................... 4
Faster Algorithms for the Nonemptiness of Streett Automata and for
Communication Protocol Pruning
M. Rauch Henzinger, J.A. Telle ................................... 61
Service-Constrained Network Design Problems
M.V. Marathe, R. Ravi, R. Sundaram ............................. 82
Approximate Hypergraph Coloring
P. Kelsen, S. Mahajan, H. Ramesh ............................... 14
Facility Dispersion and Remote Subgraphs
B. Chandra, M.M. Halld6rsson .................................... 35
The Constrained Minimum Spanning Tree Problem
R. Ravi, M.X. Goemans .......................................... 66
Randomized Approximation of the Constraint Satisfaction Problem
H.C. Lau, O. Watanabe ........................................... 67
On the Hardness of Global and Local Approximation
H. Klauck ........................................................ 88
Approximation Algorithms for the Maximum Satisfiability Problem
T. Asano, T. Ono, T. Hirata .................................... 001
On the Hardness of Approximating the Minimum Consistent OBDD
Problem
K. Hirata, S. Shimozono, A. Shinohara .......................... 211
Computing the Unrooted Maximum Agreement Subtree in
Sub-quadratic Time
T.W. Lam, W.K. Sung, H.F. Ting ............................... 421
iiiv
Greedily Finding a Dense Subgraph
Y. Asahiro, K. Iwama, H. Tamaki, T. Tokuyama ................. 631
Using Spaxsification for Parametric Minimum Spanning Tree Problems
D. Ferndndez-Baca, G. Slutzki, D. Eppstein ...................... 941
Vertex Partitioning Problems On Partial k-Trees
A. Gupta, D. Kaller, S. Mahajan, T. Shermer ................... 161
Making an Arbitrary Filled Graph Minimal by Removing Fill Edges
J.R.S. Blair, P. Heggernes, J.A. Telle ............................ 371
Sorting and Searching Revisited (Invited Lecture)
A. Andersson .................................................... 581
Lower Bounds for Dynamic Transitive Closure, Planar Point Location,
and Parantheses Matching
T. Husfeldt, T. Rauhe, S. Skyum ................................. 891
Optimal Pointer Algorithms for Finding Nearest Common Ancestors in
Dynamic Trees
S. Alstrup, M. Thorup ... ........................................ 212
Neighborhood Graphs and Distributed A + 1-Coloring
P. Kelsen ........................................................ 322
Communication Complexity of Gossiping by Packets
L. Gargano, A.A. Rescigno, U. Vaccaro .......................... 432
Optimal Cost-Sensitive Distributed Minimum Spanning Tree Algorithm
T. Przytycka, L. Higham ......................................... 642
A Linear Time Algorithm rof the Feasibility of Pebble Motion on Trees
V. Auletta, A. Monti, M. Parente, P. Persiano ................... 952
Linear-Time Heuristics rof Minimum Weight Rectangulation
C. Levcopoulos, A. Ostlin ........................................ 172
Visibility with Multiple Reflections
B. Aronov, A.R. Davis, T.K. Dey, S.P. Pal, D.C. Prasad ........ 482
XI
A Fast Heuristic for Approximating the Minimum Weight Triangulation
C. Levcopoulos, D. Krznaric ..................................... 296
Neighbours on a Grid
A. Brodnik, J.L Munro .......................................... 309
On Two Dimensional Packing
Y. Azar, L. Epstein .............................................. 321
Optimal Orthogonal Drawings of Triconnected Plane Graphs
T.C. Biedl ....................................................... 333
Walking Streets Faster
A. Ldpez-Ortiz, S. Schuierer ..................................... 345
Safe and Efficient Traffic Laws for Mobile Robots
S. Preminger, E. Upfal ........................................... 357
Progress in Selection (Invited Lecture)
M. Paterson ..................................................... 368
Probabilistic Ancestral Sequences and Multiple Alignments
G.H. Gonnet, S.A. Benner ....................................... 380
Efficient Algorithms for Lempel-Ziv Encoding
L. Ga~ieniec, M. Karpinski, W. Plandowski, W. Rytter .......... 392
The Deterministic Complexity of Parallel Multisearch
A. Bdumker, W. Dittrich, A. Pietracaprina ...................... 404
Priority Queues on Parallell Machines
G.S. Brodal ..................................................... 416
Binary Search Trees: How Low Can You Go?
R. Fagerberg ..................................................... 428
Boolean Analysis of Incomplete Examples
E. Bows, T. Ibaraki, K. Makino ................................. 440
Author Index ....................................................... 453
Derandomization Via Small Sample Spaces
Noga Alon*
School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact
Sciences, Tel Aviv University, Tel Aviv 69978, Israel. E-m~l: nogahath.tau, ac. il.
Abstract
Many randomized algorithms run successfully even when the random choices
they utilize are not fully independent. For the analysis some limited amount of
independence, like k-wise independence for some fixed k, often suffices. In these
cases, it is possible to replace the appropriate exponentially large sample spaces
required to simulate all random choices of the algorithms by ones of polynomial
size. This enables one to derandomize the algorithms, that is, convert them into
deterministic ones, by searching the relatively small sample spaces deterministi-
cally. If a random variable attains a certain value with positive probability, then
we can actually search and find a point in which it attains such a value.
The observation that n - 1 pairwise independent nontrivial random variables
can be defined over a sample space of size n has been mentioned already long ago,
see 11, 23. The pairwise independent case has been a crucial ingredient in the
construction of efficient hashing schemes in 14, 17. A more general construc-
tion, of small sample spaces supporting k-wise independent random variables,
appeared in 19. For the case of binary, uniform random variables this is treated
under the name orthogonal arrays in the Coding Theory literature, see, e.g., 27.
Most constructions are based on some simple properties of polynomials over a
finite field or on certain explicit error correcting codes.
Several researchers realized that constructions of this type are useful for
derandomizing parallel algorithms, since one may simply check all points of the
sample space in parallel. Papers pursuing this idea include 1, 22, 24, and
papers dealing with the properties of the constructions in which the sample
spaces are not necessarily uniform include 20, 21. It can be shown that for
fixed k, the minimum size of a sample space supporting n k-wise independent
random variables is f2(n k/2j ). For the binary uniform case this is essentially the
aao bound 30 (see also 12, 16), whereas for the general case it is shown in
1, where it is also observed this is tight for the binary uniform case. It follows
that polynomial size sample spaces suffice only for handling k-wise independence
for fixed k. There are, however, several ways to achieve a higher amount of
independence. One method, developed in 9 and 26, (see also 25 for related
ideas), starts with a construction of relatively small spaces which support k-wise
* Research supported in part by a USA Israeli BSF grant.
independent random variables for k = (log n) ~ and proceeds by searching
in these spaces using the conditional expectations method of 32, 29. Another
method, suggested in 31, is based on constructing spaces in which only certain
prescribed sets of random choices are independent. The third method, initiated
in 28 and improved in 3 (see also 2, 8, 13, 15) constructs sample spaces
that support random variables any k of which are nearly independent.
The above techniques have been applied in numerous papers dealing with
derandomization, and we make no attempt to list all of them here. Examples
include parallelization of derandomized geometric algorithms in 10, 18, and
various parallel graph algorithms 1, 9, 22, 24, 28. It turned out that some
variants of the techniques are also useful in derandomizing sequential algorithms
5, 7 and in designing space efficient on-line algorithms for estimating some
statistical properties of a given input sequence 4.
In the talk I will survey the basic ideas in the constructions of small sample
spaces and discuss some of the applications, focusing on various recent results
that illustrate the somewhat surprising relevance of the techniques to the solu-
tions of several algorithmic problems.
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