Table Of ContentLecture Notes in Computer Science 621
Edited by G. Goos and J. Hartmanis
Advisory Board: W. Brauer D. Gries J. Stoer
.O Nurmi E. Ukkonen (Eds.)
mhtiroglA yroehT
TAWS 29'
Third Scandinavian Workshop on Algorithm Theory
Helsinki, Finland, July 8-10, 2991
Proceedings
galreV-regnirpS
Berlin Heidelberg NewYork
London Paris Tokyo
Hong Kong Barcelona
Budapest
Series Editors
Gerhard Goos Juris Hartmanis
Universit~it Karlsruhe Department of Computer Science
Postfach 69 80 Cornell University
Vincenz-Priessnitz-Strage 1 5149 Upson Hall
W-7500 Karlsruhe, FRG Ithaca, NY 14853, USA
Volume Editors
Otto Nurmi
Esko Ukkonen
Department of Computer Scence, University of Helsinki
Teollisuuskatu 23, SF-00510 Hetsinki, Finland
CR Subject Classification (1991): E1-2, E.1-2, G.2-3
ISBN 3-540-55706-7 Springer-Verlag Berlin Heidelberg New York
ISBN 0-387-55706-7 Springer-Verlag New York Berlin Heidelberg
This work is subject to copyright. All rights are reserved, whether the whole or part of
the material is concerned, specifically the rights of translation, reprinting, re-use of
illustrations, recitation, broadcasting, reproduction on microfilms or in any other way,
and storage in data banks. Duplication of this publication or parts thereof is permitted
only under the provisions of the German Copyright Law of September 9, 1965, in its
current version, and permission for use must always be obtained from Springer-Veflag.
Violations are liable for prosecution under the German Copyright Law.
(cid:14)9 Springer-Verlag Berlin Heidelberg 1992
Printed in Germany
Typesetting: Camera ready by author/editor
Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr.
45/3140-543210 - Printed on acid-free paper
Preface
The papers in this volume were presented at SWAT '92, the Third Scandina-
vian Workshop on Algorithm Theory. The workshop, which continues the tradition
of SWAT '88, SWAT '90, and the Workshop on Algorithms and Data Structures
(WADS '89, WADS '91), is intended as an international forum for researchers in the
area of design and analysis of algorithms. The call for papers sought contributions
in algorithms and data structures, in all areas, including combinatorics, compu-
tational geometry, data bases, parallel and distributed computing, and graphics.
There were 021 papers submitted, of which the program committee selected 43 for
presentation. In addition, invited lectures were presented by Leslie .G Valiant (Di-
rect bulk-synchronous parallel algorithms), Alexander A. Razborov (On small depth
threshold circuits), Gaston Gonnet (Efficient two-dimensional searching), and Emo
Welzl (New results on linear programming and related problems).
SWAT 29' was held in ttelsinki, July 8-10, 1992, and saw organized in -oc
operation with the Department of Computer Science of the University of ttelsinki.
The organizing committee consisted of B. Aspvall (University of Bergen), .H Haf-
steinsson (University of Iceland), .R Karlsson (Lund University), E. .M Schmidt
(Aarhus University), O. Nurmi, J. Tarhio, and E. Ukkonen (University of Helsinki).
The program committee wishes to thank all referees who aided in evaluating the
papers. The organizers would like to thank J. Kivinen, .S Palander, and J. Vilo for
excellent service in all organizational matters related to the conference. Finally, we
are very grateful to Nordiska Forskarutbildningsakademin, Ministry of Education
(Finland), the Academy of Finland, University of Helsinki, EATCS, the Finnish -oS
ciety for Computer Science, NUS Microsystems ,yO and ICL Data Oy for sponsoring
the workshop.
Helsinki, May 2991 Otto Nurmi
Esko Ukkonen
Program Committee
.S Arnborg (Royal Institute of Technology)
.B Aspvall (University of Bergen)
J. Gilbert (Xerox PARC and University of Bergen)
T. Hagerup (Max-Planck-Institut)
T. Leighton (MIT)
.C Levcopoulos (Lund University)
A. Lingas (Lund University)
Th. Ottmann (University of Freiburg)
.M Overmars (University of Utrecht)
.M Penttonen (University of Joensuu)
W. Rytter (University of Warsaw)
.N Santoro (Carleton University)
.S Skyum (Aarhus University)
E. Ukkonen (chairman, University of Helsinki)
List of Referees for SWAT '92
Alt, .H Kari, J. Munthe-Kaas, E.
Anderson, .R Kari, .L Nevalainen, O.
Bang-Jensen, J. Karlsson, R. Newman, I.
Bodlaender, .H .L Karpinski, .M Nielsen, .M
Boyar, J. Katajainen, J. Nilsson, .B
Briiggemann-Klein, A. Kaufmann, .M Nurmi, O.
Carlsson, .S Kivinen, J. Orponen, .P
Casas, R. Klasing, R. Pennings, .M
Chen, J. Klein, .R Raita, T.
Chlebus, B. .S Kloks, T. Raman, R.
Cole, R. Klr T. Reich, G.
Cowen, .L J. Klugerman, .M Rossmanith, P.
de Berg, .M Knuutila, T. Schirra, .S
Dietzfelbinger, .M Kowaluk, .M Schmidt, E.
Diks, .K Kozen, .D C. Schuierer, .S
Eckerle, J. Kravets, .D Schwartzbach, .M
Fleischer, .R Krogdahl, .S Schwarzkopf, O.
Flor~en, P. Kunde, .M Singh, .M
Forsell, .M Kutytowski, .M Smid, .M
Frandsen, G. .S Lagergren, .S Syslo, .M
Garrido, O. Langemyr, .L Szymacha, T.
G~sieniec, .L Langholm, T. Tarhio, J.
Goldmann, .M Laver, T. Teia, B.
Golin, .M J. Lenhof, H.-P. Teuhola, J.
Hs J. Lisper, B. Uhrig, .C
Heinz, .A Luccio, F. van Kreveld, .M
Huber-W~chle, F. Mannila, .H Veldhorst, .M
Ihler, E. Mattsson, .C Vilo, J.
Jennings, E. Mehlhorn, K. Voutilainen, .P
Jonssons, .H Meiser, .S Wanka, R.
Kahan, .S .H Miltersen, .P B. Welzl, E.
Kant, G. Monien, .B Williamson, D. .P
Karabeg, .D Mfiller, .N Winter, P.
Table of Contents
Direct Bulk-Synchronous Parallel Algorithms (Invited)
A. V. Gerbessiotis and .51 G. Valiant .................................. 1
Memory Limited Inductive Inference Machines
R. Freivalds and C. H. Smith ........................................ 91
Retrieval of Scattered Information by EREW, CREW and CRCW PRAMs
F. Fich, M. Kowalnk, K. Lory~, M. Kntytowski, and P. Ragde ............ 03
On Small Depth Threshold Circuits (Invited)
A. A. I~azborov .................................................... 24
An Elementary Approach to Some Analytic Asymptotics
.Vi Pippenger ...................................................... 35
An Optimal Parallel Algorithm for Computing a Near-Optimal Order of
Matrix Multiplications
A. Cznmaj ........................................................ 26
Generating Sparse 2-Spanners
G. Kortsarz and D. Peleg ........................................... 73
Low-Diameter Graph Decomposition si in NC
B. Awerbuch, B. Berger, .51 Cowen, and D. Peleg ....................... 38
Parallel Algorithm for Cograph Recognition with Applications
X. He ............................................................ 49
Parallel Algorithms for All Minimum Link Paths and Link Center Problems
S. K. Ghosh and A. Maheshwari .................................... 601
Optimal Multi-Packet Routing on the Torus
M. Kaufmann and J. F. Sibeyn ..................................... 811
Parallel Algorithms for Priority Queue Operations
M. C. Pinotti and G. Pucci ........................................ 031
Heap Construction in the Parallel Comparison Tree Model
P. F. Dietz ...................................................... 041
Efficient Rebalancing of Chromatic Search Trees
J. Boyar and K. S. 15arsen ....... .................................. 151
The Complexity of Scheduling Problems with Communication Delays for Trees
A. Jakoby and R. Reischnk ......................................... 561
The List Update Problem and" the Retrieval of Sets
F. d'Amore and V. 15iberatore ...................................... 871
GKD-Trees: Binary Trees that Combine Multi-Dimensional Data Handling,
Node Size, and Fringe Reorganization
W. Cunlo and V. Yriarte .......................................... 291
Fractional Cascading Simplified
S. Sen .......................................................... 212
Dynamic -2 and 3-Connectivity on Planar Graphs
D. Giammarresi and G. F. Italiano .................................. 122
IIIV
Fully Dynamic 2-Connectivity in Planar Graphs
J. gershberger, M. Ranch, and S. Suri ............................... 233
Non-Interfering Network Flows
C. McDiarmid, B. Reed, A. Schrijver, and B. Shepherd ................. 245
Triangulating Planar Graphs While Minimizing the Maximum Degree
G. Kant and H. L. Bodlaender .................. .................... 258
How to Draw a Series-Parallel Digraph
P. Bertolazzi, R. F. Cohen, G. Di Bat~ista, R. Tamassia, and L G. Tollis. 272
Coloring Random Graphs
M. Filter and C. R. Subramanian .................................... 284
Testing Superperfection of k-Trees
T. Kloks and H. Bodlaender ........................................ 292
Parametric Problems on Graphs of Bounded Tree-Width
D. Ferndndez-Baca and G. Slutzki ................................... 304
Efficient Two-Dimensional Searching (Invited)
G. Gonnet ....................................................... 317
Improvements on Geometric Pattern Matching Problems
L. P. Chew and K. Kedem ......................................... 318
Determining DNA Sequence Similarity Using Maximum Independent Set
Algorithms for Interval Graphs
D. Joseph, J. Meidanis, and P. Tiwari ............................... 326
New Results on Linear Programming and Related Problems (Invited)
E. Weld ......................................................... 338
Dynamic Closest Pairs -- A Probabilistic Approach
M. J. Golin ...................................................... 340
Two- and Three-Dimensional Point Location in Rectangular Subdivisions
M. de Berg, M. van Kreveld, and J. Snoeyink ......................... 352
Decomposing the Boundary of a Nonconvex Polyhedron
B. Chazelle and L. Palios .......................................... 364
Convex Polygons Made from Few Lines and Convex Decompositions of
Polyhedra
J. Hershberger and J. Snoeyink ..................................... 376
Maintaining the Visibility Map of Spheres While Moving the Viewpoint
on a Circle at Infinity
H.-P. Lenhof and M. Staid ......................................... 388
Voronoi Diagrams of Moving Points in Higher Dimensional Spaces
G. Albers and T. Roos ............................................. 399
Sorting Multisets Stably in Minimum Space
J. Katajainen and T. Pasanen ...................................... 410
A Framework for Adaptive Sorting
O. Petersson and A. Moffat ............................... ......... 422
Author Index ....................................................... 434
Direct Bulk-Synchronous Parallel Algorithms *
Alexandros V. Gerbessiotis and Leslie .G Valiant
Aiken Computation Laboratory
Harvard University
Cambridge, MA 02138, USA
Abstract
We describe a methodology for constructing parallel algorithms that are
transportable among parallel computers having different numbers of processors,
different bandwidths of interprocessor communication and different periodicity
of global synchronisation. We do this for the bulk-synchronous parallel (BSP)
model, which abstracts the characteristics of a parallel machine into three nu-
merical parameters p, g, and L, corresponding to processors, bandwidth, and
periodicity respectively. The model differentiates memory that is local to a
processor from that which is not, but, for the sake of universality, does not dif-
ferentiate network proximity. The advantages of this model in supporting shared
memory or PRAM style programming have been treated elsewhere. Here we em-
phasise the viability of an alternative direct style of programming where, for the
sake of efficiency the programmer retains control of memory allocation. We show
that optimality to within a multiplicative factor close to one can be achieved for
the problems of Gauss-Jordan elimination and sorting, by transportable algo-
rithms that can be applied for a wide range of values of the parameters p, g, and
L. We also give some simulation results for PRAMs on the BSP to identify the
level of slack at which corresponding efficiencies can be approached by shared
memory simulations, provided the bandwidth parameter g is good enough.
1 The Model
The bulk-synchronous parallel or BSP model as described in [17] consists of three
parts:
(i) a number of processor/memory components. Here we will assume that each con-
sists of a sequential processor with a block of local memory.
(ii) a router that can deliver messages (typically to implement read and write opera-
tions) point to point among the components, and
(iii) facilities for globally synchronizing, in barrier style, all or a subset of the compo-
nents.
The parameters of such a machine are p, the number of processor/memory com-
ponents, L, the minimal time (measured in terms of basic local computation steps)
*This research was supported in part by the National Science Foundation under grant CCR-89-
02500 and by the Of[ice of Naval Research under grant .5440-K-58-41000N
between successive synchronization operations, and g the ratio of the total throughput
of the whole system in terms of basic computational operations, to the throughput of
the router in terms of words of information delivered.
Computation on this model proceeds in a succession of supersteps. In each super-
step each processor is given a task that can be executed using data already available
there locally before the start of the superstep. The task may include local computa-
tion steps, message transmissions and message receipts. To simplify the description of
the performance of our algorithms, in this paper we shall assume that each superstep
is either purely computation or purely communication (and not a mixture of both).
In this way the two kinds of costs are easily separated.
The model has two variants, depending on how synchronization is treated, that
affect performance to multiplicative constant factors. In one the synchronizer checks
at every L time units whether the tasks that are synchronized in the current superstep
have all finished, and only when it discerns that they have does the machine proceed
to the next superstep. In this paper, again for simplifying the analysis, we will use
the alternative model where a superstep can complete any time after the first L units.
More specifically, each superstep is charged max{L, z + hg) basic time units, where
x is the maximum number of local computational steps executed by any processor,
and h is the maximum number of packets that any processor sends or receives in that
superstep. N.B. If hi is the maximum number sent and 2h the maximum number
received we are taking h = max{hi, h2) here, although h = hi + h2 is possible too
16. Also how the expression for charging combines the z with the h is not crucial if,
as we do here, we insist that each superstep is pure computation or pure communica-
tion. We note that any particular machine may impose a lower bound on L for two
reasons: There will be a minimum time requirement for doing synchronizations. Also
the communication throughput specified by the chosen g may be realisable only for
large enough L because of startup or latency considerations in routing. We note that
although the model emphasizes global barrier style synchronization, pairs of proces-
sors are always free to synchronize pairwise by, for example, sending messages to and
from an agreed memory location. These message transmissions, however, would have
to respect the superstep rules.
2 Background
The BSP model was originally suggested as a possible "bridging" model to serve as
a standard interface between the language and architecture levels in parallel com-
putation. Two modes of programming were envisaged 17: automatic mode where
programs are written in a high level language that hides memory distribution from
the user (e.g. PRAM style), and direct mode where the programmer retains control
of memory allocation.
This paper is concerned with the direct mode. Since it is known that, under ap-
propriate conditions, automatic mode achieves optimality to within constant factors,
the primary question to ask is whether there are any circumstances at all in which
the effort of programming in direct mode is warranted. We can identify four such
circumstances:
(a) where small multiplicative constant factors in runtime are important,
(b) where smaller problem instances can be run efficiently in direct mode (i.e. less
"slack" is sufficient) than in automatic mode,
(c) where the available machine has a high g factor (since automatic mode generally
requires g to be close to unity), and
(d) where the available machine has an L that is sufficiently high for direct, but not
for automatic mode, for the problem instance in hand.
In light of the first of these conditions we emphasize multiplicative constant factors
and in this paper ew restrict ourselves to one.optimal algorithms. Although it is
generally problematic to measure complexity to this accuracy, since the operations
that are counted have to be carefully defined, it can be made meaningful, if, as we
do here, we measure ratios between runtimes on pairs of models that have the same
set of local instructions. Thus we shall say that a BSP algorithm is one-optimal ni
noitatupmoc if it performs the same number of operations, to a multiplicative factor
of 1 + o(1) as n *-- c~, as a specified corresponding sequential or PRAM algorithm.
Insistence on one-optimality leads to algorithms that only work in restricted ranges
of n and L in terms of p. These ranges can. be extended in most cases, however, if
the requirements are relaxed to, say, "two-optimality".
We note that the role of a standard bridging model is as important in the direct
programming context as in the automatic one. It will soon be inexpensive to augment
workstations and personal computers with several processors. As long as efficient
transportable software packages can be written for them, substantial reductions in
runtime can be gained. We hypothesise that the BSP model, parametrised by p,
L, and g and with direct control of memory distribution among the processors, is a
simple enough model to serve this bridging role. One can foresee software packages
to be written that can be run efficiently on a variety of machines for a wide range of
values of these parameters. In these packages the algorithms would be parametrised
by p, L, g, and the problem size n, in the same manner as we do in this paper. An
efficient instance of the algorithm can be selected by a combination of compile-time
and run-time decisions based on these parameters.
The development and analysis of direct BSP algorithms has a secondary motiva-
tion, one relating to computer architecture. A currently unresolved question is that
of determining whether, if BSP computers are constructed in currently foreseeable
technologies, it is efficacious to augment the global operations supported in hardware
beyond the router, to, for example, broadcasting or the parallel prefix. To resolve
this the complexities of some of the most frequently computed problems with respect
to these various options need to be understood.
3 Communication Optimal Simulations
In order to evaluate the usefulness of direct BSP algorithms we have to consider
the best PRAM simulations with which they might compete. This competition is
fairly stiff since, given sufficient slack, ew can find simulations that are one-optimal
in communication operations and optimal to within small multiplicative constant
factors in computational operations. By a PRAM simulation being one-optimal ni
noitacinummoc we mean in particular that T(n) read/write operations of a PRAM
Description:The papers in this volume were presented at SWAT 92, the Third Scandinavian Workshop on Algorithm Theory. The workshop, which continues the tradition ofSWAT 88, SWAT 90, and the Workshop on Algorithms and Data Structures (WADS 89, WADS 91), is intended as an international forum for researchers in th
