Table Of ContentLecture Notes in Computer Science 119
Edited by G. Goos, J. Hartmanis and J. van Leeuwen
Advisory Board: W. Brauer D. Gries J. Stoer
Ricardo Baeza-Yates Eric Goles
Patricio .V Poblete (Eds.)
LATIN '95:
Theoretical Informatics
Second Latin American Symposium
,osiaraplaV Chile, April 3-7, 1995
Proceedings
r e g n~ i r p S
Series Editors
Gerhard Goos
Universitat Karlsruhe
Vincenz-Priessnitz-StraBe 3, D-76128 Karlsruhe, Germany
Juris Hartmanis
Department of Computer Science, Cornell University
4130 Upson Hall, Ithaca, NY 14853, USA
Jan van Leeuwen
Department of Computer Science, Utrecht University
Padualaan 14, 3584 CH Utrecht, The Netherlands
Volume Editors
Ricardo Baeza-Yates
Patricio .V Poblete
Departamento de Ciencias de la Computacirn, Universidad de Chile
Blanco Encalada 2120, Casilla 2777, Santiago, Chile
Eric Goles
Departamento de Ingenierla Matem~itica, Universidad de Chile
Casilla 170-Correo 3, Santiago, Chile
CR Subject Classification (1991): El-3, E.3, G.1-2, 1.1.1-2
1991 Mathematics Subject Classification: 05Cxx, 68Qxx, 68R10
ISBN 3-540-59175-3 Springer-Verlag Berlin Heidelberg New York
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Preface
This is the proceedings volume of the International Symposium LATIN'95, Latin
American Theoretical INformatics, held in Valparaiso, Chile, April 3-7, 1995.
This event continues the tradition started by LATIN'92, organized at Sgo
Paulo, Brazil in April of 1992. The aim of the conference is to provide a high
level forum for theoretical computer science research in Latin America, and
to promote a strong and healthy interaction with the international scientific
community.
Although the LATIN conferences are intended to be comprehensive symposia
on the theory of computing, most papers accepted for LATIN'95 fell into the
following areas: complexity, cellular automata, networks, symbolic computation,
automata theory, formal languages, data structures, graph algorithms, and pat-
tern matching. In response to our call for papers, ew received 86 submissions,
from 131 authors of 22 different countries. The 83 papers in this volume were
selected on the basis of approximately 052 reports filed by the program commit-
tee and by our referees. The technical program was enhanced by the talks given
by the following invited speakers: Alberto Apostolico (Italy, USA), aosep Diaz
(Spain), a.Ian Munro (Canada), Isaac Scherson (USA), and Mike Waterman
.)ASU(
The local arrangements for the conference were handled by the Universidad
T6cnica Federico Santa Maria, from Valparaiso, and the program and organiz-
ing committee were co-chaired by Ricardo Baeza-Yates and Eric Goles, from the
Universidad de Chile, with the cooperation of the Pontificia Universidad Cat61ica
de Chile. LATIN'95 was sponsored by CONICYT Chile, Fundaci6n Andes, IFIP
SGFCS, Red Iberoamericana de Tecnologia de Software (RITOS-CYTED), and
UNESCO. Additional support was provided by ACM/SIGACT, CLEI, EATC-
S, DCC and DIM (U. de Chile), DII (UTFSM), DCC (PUC de Chile), IEEE
TCMFC, SCCC, and SBC.
We would like to thank all the individuals and organizations who cooperated
with this event and who are too numerous to be mentioned here. In particular,
the continued commitment of Springer-Verlag to publish these proceedings in
its Lecture Notes in Computer Science series has contributed strongly to the
success of this conference.
This second LATIN conference signals the consolidation of this forum as the
main Latin American event in theoretical computer science. It is a recognition
to the foresight of the people who started this initiative, especially Imre Simon,
and we feel confident that the tradition will be continued in many future LATIN
conferences.
Ricardo Baeza-Yates
Santiago, Chile, January 1995 Eric Goles
Patricio V. Poblete
Organizing Committee
Ricardo Baeza-Yates, .U ed Chile (Co-chair) Ratil Monge, UTFSM, Chile
Leopoldo Bertossi, PUC, Chile Patricio Poblete, .U de Chile
Horst yon Brand, UTFSM, Chile hnre Simon, .U ed o~S Paulo, Brazil
Alvaro Campos, PUC, Chile ollecraM Visconti, UTFSM, Chile
Eric Goles, .U de Chile (Co-chair)
Program Committee
Ricardo Baeza-Yates .U( of Chile Co-cha!rfArnaldo Moura (IBM, Brazil)
Leopoldo Bertossi (Catholic Univ., Chile) J.Ian Munro (Waterloo, Canada)
Svante Carlss0n (Lules )nedewS Gene Myers (Arizona, )ASU
Walter Cunto (IBM, )aleuzeneV Maurice Nivat (Paris, France)
Josep Diaz (Barcelona, Spain) Andrew Odlyzko (Bell Labs, USA)
rekloV Diekert (Stuttgart, Germany) ~neR Peralta (Wisconsin, USA)
Vladimir Estivill-Castro (LANIA, )ocixeM Dominique Perrin (Paris, France)
Joachim nov zur Gathen (Toronto, Canada) Patricio Poblete .U( of Chile)
Eric Goles .U( of Chile, )riahc-oC Gregory Rawlins (Indiana, USA)
Gast6n Gonnet (ETH, Switzerland) Antonio Restivo (Palermo, Italy)
Jozef Gruska (Bratislava, )aikavolS zrogezrG Rozenberg (Leiden, Netherlands)
Jan nav Leeuwen (Utrecht, Netherlands) Isaac Scherson (Irvine, )ASU
Tom Leighton (MIT, )ASU Imre Simon (S~o Paulo, Brazil)
Andrzej Lingas (Lund, )nedewS Godfried Toussaint (McGill, Canada)
Laszlo Lovasz (Yale, )ASU oiviN Ziviani (Minas Gerais, Brazil)
List of Referees
E.F. Barbosa .R Gavalda J. Meidanis J. Stolfi
R.S. Bigonha .A dlowenorG .A llohcsuM .R Subramanian
C. Bliek H.J. moobegooH .K Reinhardt .A Teruel
.H Bodlaender .~h Jantzen .W regrebnessieR J. Tor~n
.M ed Carvalho .E Jennings M.C. Rivara N.J. Vieira
.O Carvalho .B Kurshan J.C. Setubal
W. hcsoD J.M. da Mata P.S. ed Souza
Table of Contents
Visibility Graphs of 2-Spiral Polygons ....................................... 1
James Abello, Krishna Kumar
Random Generation of Colored Trees ...................................... 61
L. Alonso, R. Schott
Space Filling Curves and Their Use in the Design of Geometric
Data Structures ........................................................... 36
Tetsuo Asano, Desh Ranjan, Thomas Roos, Emo Welzl, Peter Widmayer
Tight Bounds for Finding Degrees from the Adjacency Matrix .............. 49
R. Balasubramanian, Venkatesh Raman, G. Srinivasaraghavan
Lower Bounds for Modular Counting by Circuits with Modalar Gates ....... 60
David Mix Barrington, Howard Straubing
On the Relation Between BDDs and FDDs .................. : ............. 72
Bernd Beeker, Rolf Drechsler, Ralph Werchner
On Dynamical Properties of Generalized Toggle Automata .................. 84
F. Blanchard, Alejandro Maass
Free Shuffle Algebras in Language Varieties ................................ 99
Stephen L. Bloom, Zolts ~sik
Lower Bounds for the Matriz Chain Ordering Problem .................... 112
Phillip G. Bradford, Venkatesh Choppella, Gregory J.E. Rawlins
Off-Line Electronic Cash Based on Secret-Key Certificates ................ 131
Stefan Brands
Recognizable Sets of Numbers in Nonstandard Bases ...................... 167
V6ronique Bruy6re, Georges Hansel.
On Weak Growing Context-Sensitive Grammars .......................... 180
Gerhard Buntrock, Gundula Niemann
Logic of Plotkin Continuous Domain ..................................... 195
Benjamin R. Callejas Bedregal, Benedito Melo Aci61y
(Probabilistie) Recurrence Relations Revisited ............................. 207
Shiva Chaudhuri, Devdatt Dubhashi
IIIV
On Linear-Time Alphabet-Independent 2-Dimensional Pattern Matching .. 220
Maxime Croehemore, Wojcieeh Rytter
Reversible Cellular Automaton Able to Simulate Any Other Reversible
One Using Partitioning Automata ........................................ 230
J~r6me Durand-Lose
Nearest Neighbour Graph Realizability is NP-hard ......................... 245
Peter Eades, Sue Whitesides
Linear-Time Algorithms for Parametric Minimum Spanning Tree
Problems on Planar Graphs .............................................. 257
David Fern~ndez-Baca, Giora Slutzki
Paging More Than One Page ............................................. 272
Esteban Feuerstein
On Edge-Colouring Indifference Graphs .................................. 286
Celina M. Herrera de Figueiredo, Joho Meidanis, Celia Picinin de Mello
On the Approximability of Some Maximum Spanning Tree Problems ....... 300
Giulia Galbiati, Angelo Morzenti, Francesco Maffioli
Gauss Periods and Fast Exponentialiou in Finite Fields .................. 311
Shuhong Gao, Joachim von zur Gathen, Daniel Panario
Unbounded Search and Recursive Graph Problems ......................... 323
William I. Gasarch, Katia S. Guimarges
On the Complexity of Computing the Greatest Common Divisor of Several
Univariate Polynomials .................................................. 332
Laureano Gonzs
State Complexity of SBTA Languages .................................... 346
Jozef Gruska, Angelo Monti, Margherita Napoli, Domenico Parente
Pushdown Automata with Bounded Nondeterminism
and Bounded Ambiguity .................................................. 358
Christian Herzog
Multihead Two- Way Probabilistic Finite Automata ........................ 371
Ioan I. Macarie
Non-Erasing Turing Machines: a New Frontier Between a Decidable Halting
Problem and Universality ................................................ 386
Maurice Margenstern
(cid:141)I
Cyclic Automata Networks on Finite Graphs .............................. 398
Martin Matamala, Eric Goles
Multiple Alignment of Biological Sequences with Gap Flexibility ........... 411
Jo~o Meidanis, Jo~o C. Setubal
Lower Bounds for the Modular Communication Complexity of Various
Graph Accessibility Problems ............................................. 427
Christoph Meinel, Stephan Waack
On Monotonous Oracle Machines ........................................ 436
M. Mundhenk
On Using Learning Automata for Fast Graph Partitioning ................ 449
B. John Oommen, Edward V. de St. Croix
Solution of a Problem of Yekutieli and Mandelbrot ........................ 461
Helmut Prodinger
A Rewrite Approach for Constraint Logic Programming ................... 469
Gilles Richard, Frederic Saubion
Simulations Between Cellular Automata on Cayley Graphs ................ 483
Zsuzsanna R6ka
A Temporal Logic for Real-Time Partial-Ordering with Named
Transactions ............................................................. 494
Farn Wang
A New Approach for Routing in Arrangement Graphs and
Its Performance Evaluation .............................................. 509
Peter M. Yamakawa, Hiroyuki Ebara, Hideo Nakano
Author Index ............................................................ 525
Visibility Graphs of 2-Spiral Polygons
dednetxE( )tcartsbA
James Abello ,1 and Krishna Kumar 2
Department of Computer Science, Texas A&M University, College Station, TX
77843, USA
2 Department of Mathematics and Computer Science
Colby College, Waterville, ME 04901, USA.
Abstract. In a previous paper, the authors reduced the characterization
of visibility graphs of simple polygons to the coordinatization of certain
uniform rank 3 oriented matroids. We show here that in the case of 2-
spiral polygons such coordinatization is possible therefore characterizing
visibility graphs of 2-spiral polygons.
1 Introduction
Two vertices of a simple polygon are called visible if the open line segment
between them is either an edge of P, or is completely contained in the interior
of the polygon. The visibility graph of a polygon is the graph whose vertices
correspond to the vertices of the polygon and edges correspond to visible pairs of
vertices in the polygon. Visibility graphs are fundamental structures in compu-
tational geometry, and find application in areas such as graphics 8 and robotics
6, yet very little is known about their combinatorial structure. From the com-
putational standpoint, the complexity of the recognition problem for visibility
graphs is only known to be in PSPACE 3. It is not known to be in NP nor
is it known to be NP-complete.
It is known that visibility graphs do not lie in any of the well known classes
of graphs such as planar graphs, perfect graphs etc. ,3 5. The first set of neces-
sary conditions for a graph to be a visibility graph were obtained by Ghosh 5
and several stronger versions have been proposed. O'Rourke 7 has an excellent
account of this research. We concentrat~ here in the set of conditions offered in
1 because they are sufficient to construct, from the graph, a uniform oriented
matroid of rank 3. It is shown there that it suffices to exhibit an affine coor-
dinatization of these matroids in order to obtain a characterization of visibility
graphs of simple polygons. This characterization could settle the complexity of
this decade old question. In this paper, we prove that in the case of 2-spiral poly-
gons the conditions of 1 are enough to reconstruct a polygon from the graph.
The obtained characterization has a natural generalization to k-spiral polygons
for k > 3.
* Work partiaJy supported by NSF grants No: DCR-8603722 and DCR-8896281
Section 2 contains the relevant definitions and states the main results of 1J.
Section 3 presents our characterization of visibility graphs of 2-spiral polygons
and points out the main difficulties in its generalization.
2 Definitions
It is clear that every visibility graph is Hamiltonian and we therefore restrict our
attention to Hamiltonian graphs. We further assume that the graphs considered
are undirected, loopless and without multiple edges.
Let G = (V, E) be a Hamiltonian graph with a prescribed Hamiltonian cycle
H. The vertices of G are labelled along H from 0 to n - 1. The vertex labelled
i is denoted vi. vi-1 and Vi+l denote the predecessor and successor of vi on H,
respectively. All subscript arithmetic is modulo n. It is convenient to think of
G as being embedded in the plane so that H forms a simple closed curve. In this
setting, a traversal of H from vi to vj in the order vi, Vi+l,..., vj-1, vj may be
thought of as a counterclockwise traversal of H, and the traversal that goes from
vi to vj in the order vi, vi-1,..., Vj+l, yj corresponds to clockwise traversals.
In this paper, unless specified otherwise, traversals of H are implicitly assumed
to be in counterclockwise order. A vertex vr in a Hamiltonian graph G is called
an ear if vr-1 is adjacent to Vr+l in G.
For any two vertices vi and vj, the set {Yi, Vi+I,...,Vj_I,Vj} of vertices
encountered in traversing H from vi to vj, is called the chain from vi to vj
and is denoted chainv/, vj. This set of vertices constitutes a simple path in G.
The chain from Vi+l to vj-1 is denoted chain(vi, vj). We also use chainvi, vj)
and chain(vl, vj in the obvious manner. We emphasize that chain(v/, va) and
chain(vk,vl) are always disjoint sets. We say that vi < vj < vk if vj lies on
chain(v/, vk).
Two vertices vi and vj of G are said to be invisible if viv i E E. For an
invisible pair vi, vk, a vertex vj is called an inner blocking vertex 5, relative
to H, if vj lies on chain(vi, vk) and vxv v E E for all v, on chainvi, vj) and
v v on chain(vj, vk. Similarly, a vertex vj is called an outer blocking vertex
relative to H for the invisible pair viva ifvj lies on chain(vk, vi) and v,v~ E E
for all v~ on chain(vj, vi and v v on chainva, vj). In general, vj is called a
blocking vertex for the invisible pair viva if it is either an inner or an outer
blocking vertex for this pair.
A simple path P = uoul ... u~ is called an ordered path relative to H, if
the vertices in P are encountered in the order uo, us,..., ur when His traversed
from u0. Similarly, a simple cycle C = UoUl (cid:12)9 (cid:12)9 (cid:12)9 UrUo is called an ordered cycle
relative to H if the vertices in C are encountered in the order Uo, ul,.., ur, uo
(or its reverse) when H is traversed from u0. Two pairs vivj and vavl, are said to
be separable 5 with respect to a vertex pV if both vi and vj are encountered
before vk and vt ( or vice versa), when H is traversed from vp. In this case,
we say that vivj and vkvz are vp-separable; otherwise we say that they are
vp-inseparable.
