Table Of ContentLecture Notes in Computer Science 1203
Edited by G. Goos, J. Hartmanis and J. van Leeuwen
Advisory Board: W. Brauer D. Gries J. Stoer
Giancarlo Bongiovanni Daniel Pierre Bovet
Giuseppe Di Battista (Eds.)
smhtiroglA
dna ytixelpmoC
Third Italian Conference, CIAC '97
Rome, Italy, March 12-14, 1997
Proceedings
r e g n ~ i r p S
Series Editors
Gerhard Goes, Karlsruhe University, Germany
Juris Hartmanis, Comell University, NY, USA
Jan van Leeuwen, Utrecht University, The Netherlands
Volume Editors
Giancarlo Bongiovanni
Daniel Pierre Bovet
Giuseppe Di Battista
University of Rome "La Sapienza"
Via Salaria 113, 1-00198 Rome, Italy
E-mail: ciac97 @dsi.uniroma 1.it
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Die Deutsche Bibliothek - CIP-Einlaeitsaufnahme
Algorithms and complexity ' third Italian conference ; proceedings / CIAC, '97,
Rome, Italy, March 21 - ,41 1997. Gianearlo Bongiovanni ... (ed.). - Berlin ;
Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ;
Paris ; Santa Clara ; Singapore ; Tokyo" Springer, 1997
erutceL( seton in retupmoc ecneics ; )3021
ISBN 5-29526-045-3
NI~: CIAC <3, 1997, Reran>; Bortgiovanni , Gianearlo t-Irsg.; GT
CR Subject Classification (1991): F.1-2, E.1, 1.3.5, G.2
ISSN 0302-9743
ISBN 3-540-62592-5 Springer-Verlag Berlin Heidelberg New York
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(cid:14)9 Springer-Verlag Berlin Heidelberg 1997
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Preface
The papers in this volume were presented at the Third Italian Conference on
Algorithms and Complexity (CIAC '97). The Conference took place on March
12-14, 1997 in Rome (Italy).
International CIAC Conferences present research contributions in theory and
applications of sequential, parallel, and distributed algorithms, data structures,
and computational complexity , and are held at the Conference Center of the
University of Rome "La Sapienza"
In response to the Call for Papers, 47 were submitted. From these submissions,
the Program Committee selected 52 for presentation at the Conference. In ad-
dition to the selected papers, Gianfranco Bilardi, Shimon Even, and Christos
Papadimitriou were invited to give plenary lectures.
We wish to thank all the members of the Program Committee and of the Orga-
nizing Committee, the plenary lecturers who accepted our invitation to speak,
all those who submitted papers for consideration, and all the referees.
Rome, January 1997 Giancarlo Bongiovanni
Daniel Pierre Bovet
Giuseppe Di Battista
IV
Organizing Committee:
D.P. Bovet (Rome, chair) .S De Agostino (Rome)
G. Bongiovanni (Rome) R. Silvestri (Rome)
A. Clementi (Rome)
Program Committee:
G. Di Battista (Rome, chair) L. Pagli (Pisa)
H. Bodlaender (Utrecht) G. Persiano (Salerno)
D. Breslauer (Aarhus) R. Petreschi (Rome)
P. Crescenzi (Rome) J. Rolim (Geneva)
T. Hagerup (Saarbriicken) .S Whitesides (Montreal)
G. Italiano (Venice)
Additional Referees:
A. Andreev P. Ferragina K. Mehlhorn R. Seidet
V. Auletta .A Ferreira R. Milanese J. Sibeyn
P. Bertolazzi R. Fleischer A. Monti R. Silvestri
T. Biedl P. Flocchini N. Nishimura .M Smid
M.A. Bonuccelli .A Galluccio J. O'Rourke D. Sosnowska
.A Brogi N. Garg .S Orlando G. Tel
T. Calamoneri L. Gargano .M Papatriantafilou D. neir@hT
B. Carpentieri L. Gasieniec .M Parente L. Toniolo
.M Cesati R. Galvad~ A. Pedrotti G. Toussaint
J. Cheriyan J. Gergov .M Pelillo L. Trevisan
B. Chopard D. Giammarresi C. Petrioli P. Tsigas
P. Cignoni R. Grossi A. Piperno E. Urland
.A Clementi J.L. Tr~ff V. Priebe U. Vaccaro
B. Codenotti H.P. Lenhof T. Przytycka .M van Kreveld
.A Cortesi G. Lenzini .A Rescigno .M Veldhorst
.A Cresti G. Liotta F. Romani R. Veltkamp
.S De Agostino E. Lodi C. Rfib T. Warnow
.M de Berg G. Lotti .A Salibra .S Wismath
.M Di Ianni F. Luceio V. Scarano .M Yung
D. Dubhashi L. Margara .S Schirra A. Zemach
P. Favati A. Massini .U SchSning
Sponsored by:
Dipartimento di Scienze dell'Informazione, Universit~ di Roma "La Sapienza"
Universit~ degli Studi di Roma "La Sapienza"
Table of Contents
Invited Presentations
Algorithms and Data Structures for Control Dependence and Related
Compiler Problems 1
.G Bilardi
Embedding Interconnection Networks in Grids via the Layered
Cross Product 3
.G Even, S. Even
Regular Presentations
Finding Optimum k-vertex Connected Spanning Subgraphs:
Improved Approximation Algorithms for k = 3, 4, 5 31
Y. Dinitz, Z. Nutov
The Optimum Cost Chromatic Partition Problem 25
K. Jansen
Fault Tolerant K-Center Problems 37
S. Khuller, R. Pless, Y.J. Sussmann
_~R N (NP) Distinguishes Robust Many-One and Turing Completeness 49
E. Hemaspaandra, L.A. Hemaspaandra, H. Hempel
Syntactic Characterization in LISP of the Polynomial Complexity
Classes and Hierarchy 16
S. Caporaso, M. Zito, N. Galesi, E. Covino
On the Drift of Short Schedules 74
.U Feige, .G Rayzman
On Removing Non-degeneracy Assumptions in Computational Geometry 86
F. GSmez, S. Ramaswami, .G Toussaint
Maintaining Maxima under Boundary Updates 001
F. d'Amore, P.G. Franciosa, R. Giaccio, M. Talamo
An Optimal Algorithm for One-Separation of a Set of Isothetic Polygons 011
A. Datta, K. Krithivasan, T. Ottmann
Nice Drawings for Planar Bipartite Graphs 221
.U Fb'flmeier, M. Kaufmann
Area Requirement of Gabriel Drawings 531
.G Liotta, R. Tamassia, I.G. Tollis, P. accoV
Design of Reliable Combinatorial Algorithms Using Certificates 147
F. Luccio, A. Pedrotti
viii
An Improved Deterministic Algorithm for Generalized Random Sampling 951
A. Amir, E. Dar
Polynomial Time Algorithms for Some Self-Duality Problems 171
.C Domingo
A Note on Updating Suffix Tree Labels 181
P. Ferragina, R. Grossi, .M Montangero
Relaxed Balanced Red-Black Trees 391
.S Hanke, .T Ottmann, .E Soisalon-Soininen
The Algorithmic Complexity of Chemical Threshold Testing 502
P. Damaschke
A Meticulous Analysis of Mergesort Programs 712
J. Katajainen, J.L. Triiff
BSP-Like External-Memory Computation 922
Y.F. Sibeyn, .M Kaufmann
Topological Chaos for Elementary Cellular Automata 142
.G Cattaneo, .M Finelli, L. aragraM
On the Complexity of Balanced Boolean Functions 352
A. Bernasconi
On Sets with Easy Certificates and the Existence of One-Way
Permutations 462
L.A. ~ardnaapsameH .J Rothe, .G Weehsung
Isomorphism for Graphs of Bounded Distance Width 672
K. Yamazaki, H.L. Bodlaender, B. ed Fluiter, D.M. Thilikos
Hardness of Approximating Problems on Cubic Graphs 882
P. Alimonti, .V Kann
Tree Contractions and Evolutionary Trees 992
M.- Y. Kao
Author Index 113
Algorithms and Data Structures for Control
Dependence and Related Compiler Problems
Gianfranco Bilardi
DEI, Utfiversi~ di Padova, 35131 Padova, Italy, and
EECS, University of Illinois, Chicago, IL 60607
Abstract
The control dependence relation plays a fundamental role in program restruc-
turing and optimization. It is used in many phases of modern compilers, Such
as dataflow analysis, loop transformations, and code scheduling. This talk will
survey recent results coacerning the efficient computation of control dependence
information for a given program. The concrete application of these results to
the problem of obtaining the static single assignment form for a program will
be discussed. Finally, a framework will be outlined that generalizes the classical
notion of control dependence to include othm" interesting variants. The talk is
largely based on joint work with Keshav Pingali ,1 2, 3, 4.
Technically, control dependence is a relation between nodes and edges of
the control flow graph (CFG) of a program, a directed graph in which nodes
represent statements, and an edge u +-- v represents possible flow of control from
u to v. A node w E V is said to be control dependent on edge (u +-- v) E E if w
postdominates v, and if w r u, then w does not postdominate u.
Several applications of control dependence require the computation of sets
of the following type: cd(e), which is the set of statements control dependent on
control-ttow edge e; concls(w), which is the set of edges on which statement w
is dependent, and cdequiv(w), which is the set of statements having the same
control dependences as w.
A novel data structure is introduced, the detnemgua postdominator tree (.APT),
which can be constructed in space and time proportional to the size of the
program, and which supports enumeration of the above mentioned control-
dependence sets in time proportional to their size. Hence, APT provides an
optimal representation of control .ecnedneped
By exploiting the well known relation between control dependence and dom-
inance frontiers, the APT is used to develop an algorithm for the single static
assignment form of a program, which takes linear time per variable.
Finally, a notion of generalized dominance is introduced, based on a para-
metric set of paths in the control flow graph. This new definition leads to a
generalized notion of control dependence, which includes standard control -ed
pendence and weak control dependence as special cases. To illustrate the utility
of the framework, it is shown how the APT can be used for the optimal com-
putation of weak control dependence sets.
References
1 K. Pingali and G. Bilardi. APT: A data structure for optimal control depen-
dence computation. In Proc. A CM SIGPLAN '95 Conference on Programming
Language Design and Implementation (PLDI), pages 32-46, La Jolla, Califor-
nia, June 1995.
2 G. Bilardi and K. Pingali, A generalized framework for control dependence,
In Proc. ACM SIGPLAN '96 Conference on Programming Language Design
and Implementation (PLDI), pages 291-300, Philadelphia, Pennsylvania, May
1996.
*
K. Pingali and G. Bilardi. Optimal control dependence computation and the
Roman chariots problem. A CM Transactions on Programming Languages and
Systems. To appear.
4 G. Bilardi and K. Pingali. Computing the single static assignment form of
programs. Manuscript. October 1996.
Embedding Interconnection Networks in Grids
via the Layered Cross Product
Guy Even I and Shimon Even 2
1 Universitaet des Saarlandes, FB 41 Informatik, Lehrstuhl Prof. Paul, Postfach
51 11 50, 66041 Saarbriicken, Germany. e-mail: guy0cs.uni-sb.de
U RL: http ://www-wjp. cs. uni-sb, de/,,~guy/
2 Bell-Labs, Lucent Technologies, 007 Mountain Ave., Murray Hill, NJ 07974. On
leave from the Computer Sci. Dept., Technion - Israel Inst. of Tech., Haifa, Israel
32000. Research was partly supported by the United States -Israel Binational Science
Foundation, grant No. 94-00266/1. e-mail: even0research.bell-labs.com
Abstract. A technique for automatically producing a rectilinear planar
drawings of interconneetion networks is described. It is based on the
Layered Cross Product suggested by Even and Litman. The technique is
demonstrated on the Butterfly network, the binary tree and the Mesh-
of-Trees of Leighton.
1 The Layered Cross Product
Many layered graphs are known to be useful as interconnection networks. Exam-
ples are the Butterfly network, including all its different looking representations,
meshes of trees, Fat-trees, the Beneg network, multibutterflies.
In 4, Even and Litman introduced the concept of Layered Cross Product,
LCP, of layered graphs and showed that several of the important and well known
networks are LCP-s of simple layered graphs, such as trees. Following is the
definition of LCP from 4.
A layered graph, ofg + 1 layers, G = (%, Vi,..., ~, E), consists of:
- ~ + 1 layers of vertices; iV is the (nonempty) set of vertices in layer i.
- E is a set of directed edges. Every edge (u, }v connects two vertices of two
adjacent layers; i.e. if u G :~V then v C V~+I.
Let G l, G 2 be layered graphs of ~ + 1 layers each; i.e., for j C {1, 2}, G j =
(Y j, vJ,..., V/,EJ). Their Layered Cross Product, LCP, G 1 (cid:141) G 2 is a layered
graph, G = (V0, Vi,..., (cid:1)89 E), where:
