DuongThanCong.com Lecture Notes in Computer Science Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M Kleinberg Cornell University, Ithaca, NY, USA Friedemann Mattern ETH Zurich, Switzerland John C Mitchell Stanford University, CA, USA Oscar Nierstrasz University of Bern, Switzerland C Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen University of Dortmund, Germany Madhu Sudan Massachusetts Institute of Technology, MA, USA Demetri Terzopoulos New York University, NY, USA Doug Tygar University of California, Berkeley, CA, USA MosheY.Vardi Rice University, Houston, TX, USA Gerhard Weikum Max-Planck Institute of Computer Science, Saarbruecken, Germany CuuDuongThanCong.com 3059 Springer Berlin Heidelberg New York Hong Kong London Milan Paris Tokyo CuuDuongThanCong.com Celso C Ribeiro Simone L Martins (Eds.) Experimental and Efficient Algorithms Third International Workshop, WEA 2004 Angra dos Reis, Brazil, May 25-28, 2004 Proceedings Springer CuuDuongThanCong.com eBook ISBN: Print ISBN: 3-540-24838-2 3-540-22067-4 ©2005 Springer Science + Business Media, Inc Print ©2004 Springer-Verlag Berlin Heidelberg All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Springer's eBookstore at: and the Springer Global Website Online at: CuuDuongThanCong.com http://ebooks.springerlink.com http://www.springeronline.com Preface The Third International Workshop on Experimental and Efficient Algorithms (WEA 2004) was held in Angra dos Reis (Brazil), May 25–28, 2004 The WEA workshops are sponsored by the European Association for Theoretical Computer Science (EATCS) They are intended to provide an international forum for researchers in the areas of design, analysis, and experimental evaluation of algorithms The two preceding workshops in this series were held in Riga (Latvia, 2001) and Ascona (Switzerland, 2003) This proceedings volume comprises 40 contributed papers selected by the Program Committee along with the extended abstracts of the invited lectures presented by Richard Karp (University of California at Berkeley, USA), Giuseppe Italiano (University of Rome “Tor Vergata”, Italy), and Christos Kaklamanis (University of Patras, Greece) As the organizer and chair of this wokshop, I would like to thank all the authors who generously supported this project by submitting their papers for publication in this volume I am also grateful to the invited lecturers, who kindly accepted our invitation For their dedication and collaboration in the refereeing procedure, I would like also to express my gratitude to the members of the Program Committee: E Amaldi (Italy), J Blazewicz (Poland), V.-D Cung (France), U Derigs (Germany), J Diaz (Spain), M Gendreau (Canada), A Goldberg (USA), P Hansen (Canada), T Ibaraki (Japan), K Jansen (Germany), S Martello (Italy), C.C McGeoch (USA), L.S Ochi (Brazil), M.G.C Resende (USA), J Rolim (Switzerland), S Skiena (USA), M Sniedovich (Australia), C.C Souza (Brazil), P Spirakis (Greece), D Trystram (France), and S Voss (Germany) I am also grateful to the anonymous referees who assisted the Program Committee in the selection of the papers to be included in this publication The idea of organizing WEA 2004 in Brazil grew out of a few meetings with José Rolim (University of Geneva, Switzerland) His encouragement and close collaboration at different stages of this project were fundamental for the success of the workshop The support of EATCS and Alfred Hofmann (Springer-Verlag) were also appreciated I am thankful to the Department of Computer Science of Universidade Federal Fluminense (Niterói, Brazil) for fostering the environment in which this workshop was organized I am particularly indebted to Simone Martins for her invaluable support and collaboration in the editorial work involved in the preparation of the final camera-ready copy of this volume Angra dos Reis (Brazil), May 2004 CuuDuongThanCong.com Celso C Ribeiro (Chair) This page intentionally left blank CuuDuongThanCong.com Table of Contents A Hybrid Bin-Packing Heuristic to Multiprocessor Scheduling Adriana C.F Alvim, Celso C Ribeiro Efficient Edge-Swapping Heuristics for Finding Minimum Fundamental Cycle Bases Edoardo Amaldi, Leo Liberti, Nelson Maculan, Francesco Maffioli 14 Solving Chance-Constrained Programs Combining Tabu Search and Simulation Roberto Aringhieri 30 An Algorithm to Identify Clusters of Solutions in Multimodal Optimisation Pedro J Ballester, Jonathan N Carter 42 On an Experimental Algorithm for Revenue Management for Cargo Airlines Paul Bartodziej, Ulrich Derigs 57 Cooperation between Branch and Bound and Evolutionary Approaches to Solve a Bi-objective Flow Shop Problem Matthieu Basseur, Julien Lemesre, Clarisse Dhaenens, El-Ghazali Talbi Simple Max-Cut for Split-Indifference Graphs and Graphs with Few Hans L Bodlaender, Celina M.H de Figueiredo, Marisa Gutierrez, Ton Kloks, Rolf Niedermeier A Randomized Heuristic for Scene Recognition by Graph Matching Maria C Boeres, Celso C Ribeiro, Isabelle Bloch 72 87 100 An Efficient Implementation of a Joint Generation Algorithm 114 Endre Boros, Khaled Elbassioni, Vladimir Gurvich, Leonid Khachiyan Lempel, Even, and Cederbaum Planarity Method John M Boyer, Cristina G Fernandes, Alexandre Noma, José C de Pina* A Greedy Approximation Algorithm for the Uniform Labeling Problem Analyzed by a Primal-Dual Technique Evandro C Bracht, Luis A.A Meira, Flávio K Miyazawa Distributed Circle Formation for Anonymous Oblivious Robots Ioannis Chatzigiannakis, Michael Markou, Sotiris Nikoletseas CuuDuongThanCong.com 129 145 159 VIII Table of Contents Dynamic Programming and Column Generation Based Approaches for Two-Dimensional Guillotine Cutting Problems Glauber Cintra, Yoshiko Wakabayashi Engineering Shortest Path Algorithms Camil Demetrescu, Giuseppe F Italiano 175 191 How to Tell a Good Neighborhood from a Bad One: Satisfiability of Boolean Formulas Tassos Dimitriou, Paul Spirakis 199 Implementing Approximation Algorithms for the Single-Source Unsplittable Flow Problem Jingde Du, Stavros G Kolliopoulos 213 Fingered Multidimensional Search Trees Amalia Duch, Conrado Martínez Faster Deterministic and Randomized Algorithms on the Homogeneous Set Sandwich Problem Celina M.H de Figueiredo, Guilherme D da Fonseca, Vinícius G.P de Sá, Jeremy Spinrad 228 243 Efficient Implementation of the BSP/CGM Parallel Vertex Cover FPT Algorithm Erik J Hanashiro, Henrique Mongelli, Siang W Song 253 Combining Speed-Up Techniques for Shortest-Path Computations Martin Holzer, Frank Schulz, Thomas Willhalm 269 Increased Bit-Parallelism for Approximate String Matching Heikki Hyyrö, Kimmo Fredriksson, Gonzalo Navarro 285 The Role of Experimental Algorithms in Genomics Richard M Karp 299 A Fast Algorithm for Constructing Suffix Arrays for Fixed-Size Alphabets Dong K Kim, Junha Jo, Heejin Park 301 Pre-processing and Linear-Decomposition Algorithm to Solve the k-Colorability Problem Corinne Lucet, Florence Mendes, Aziz Moukrim 315 An Experimental Study of Unranking Algorithms Conrado Martínez, Xavier Molinero CuuDuongThanCong.com 326 Table of Contents An Improved Derandomized Approximation Algorithm for the Max-Controlled Set Problem Carlos A Martinhon, Fábio Protti GRASP with Path-Relinking for the Quadratic Assignment Problem Carlos A.S Oliveira, Panos M Pardalos, Mauricio G.C Resende IX 341 356 Finding Minimum Transmission Radii for Preserving Connectivity and Constructing Minimal Spanning Trees in Ad Hoc and Sensor Networks Francisco Javier Ovalle-Martínez, Ivan Stojmenovic, Fabián García-Nocetti, Julio Solano-González 369 A Dynamic Algorithm for Topologically Sorting Directed Acyclic Graphs David J Pearce, Paul H.J Kelly 383 Approximating Interval Coloring and Max-Coloring in Chordal Graphs Sriram V Pemmaraju, Sriram Penumatcha, Rajiv Raman 399 A Statistical Approach for Algorithm Selection Joaquín Pérez, Rodolfo A Pazos, Juan Frausto, Guillermo Rodríguez, David Romero, Laura Cruz An Improved Time-Sensitive Metaheuristic Framework for Combinatorial Optimization Vinhthuy Phan, Steven Skiena A Huffman-Based Error Detecting Code Paulo E.D Pinto, Fábio Protti, Jayme L Szwarcfiter 417 432 446 Solving Diameter Constrained Minimum Spanning Tree Problems in Dense Graphs Andréa C dos Santos, Abílio Lucena, Celso C Ribeiro 458 An Efficient Tabu Search Heuristic for the School Timetabling Problem Haroldo G Santos, Luiz S Ochi, Marcone J.F Souza 468 Experimental Studies of Symbolic Shortest-Path Algorithms Daniel Sawitzki Experimental Comparison of Greedy Randomized Adaptive Search Procedures for the Maximum Diversity Problem Geiza C Silva, Luiz S Ochi, Simone L Martins Using Compact Tries for Cache-Efficient Sorting of Integers Ranjan Sinha CuuDuongThanCong.com 482 498 513 A Heuristic for Minimum-Width Graph Layering 573 layers (horizontal levels) Naturally, drawings with low edge density are clear and easier to comprehend Minimum-Width DAG Layering Clearly, it is trivial to find a layering of a DAG with the minimum width if the width of a layer is considered equal to the sum of the widths of the original DAG nodes in that layer In this case any layering with a single node per layer has the minimum width However, such a definition of width does not approximate the width of the final drawing because the space occupied by long edges is not insignificant (see Figure 2) The contribution of the long edges to the layering width can be taken into account by assigning positive width to the dummy nodes and taking them into when computing the layering width It is sensible to assume that the dummy nodes occupy smaller space than the original DAG nodes especially in DAGs which come from practical applications and may have large node labels Fig A hierarchical drawing of a DAG The black circles are the original DAG nodes and the smaller white squares are the dummy nodes along long edges All edges point downwards It is NP-hard to find a layering with the minimum width when the contribution of the dummy nodes is taken into account [2] The first attempt to solve this problem by a heuristic algorithm belongs to Branke et al [1] They proposed a polynomial-time heuristic which did not meet their expectations about quality when tested with relatively small graphs To the best of our knowledge the only method that can be used for minimum-width DAG layering is the branch-andcut algorithm of Healy and Nikolov which takes as an input an upper bound on the width and produces a layering subject to it (if feasible) [8] Although exact, the algorithm of Healy and Nikolov is very complex to implement and its running time is exponential in the worst case In this work we design a simple polynomial-time algorithm which finds narrow layerings We call it MinWidth Similar to the algorithm of Branke et al it is a heuristic and it does not guarantee the minimum width Nevertheless it produces layerings which are narrower than the layerings produced by any of the CuuDuongThanCong.com 574 A Tarassov, N.S Nikolov, and J Branke known polynomial-time layering algorithms In the remainder of this section we introduce the initial rough version of MinWidth which we tune and extensively test in Section 3.1 The Longest-Path Algorithm We base MinWidth on the longest-path algorithm displayed in Algorithm The longest-path algorithm constructs layerings with the minimum height equal to the number of nodes in the longest directed path It builds a layering layer by layer starting from the bottom layer labeled as layer This is done with the help of two node sets U and Z which are empty at start The value of the variable current_layer is the label of the layer currently being built As soon as a node gets assigned to a layer it is also added to the set U Thus, U is the set of all nodes already assigned to a layer Z is the set of all nodes assigned to a layer below the current layer A new node to be assigned to the current layer is picked among the nodes which have not been already assigned to a layer, i.e and which have all their immediate successors assigned to the layers below the current one, i.e 3.2 A Rough Version of MinWidth In the following, we will assume that all dummy nodes have the same width, although our considerations can be easily generalized to variable dummy node widths We will also assume that is the width of node We start with an initial rough version of MinWidth , displayed in Algorithm 2, which CuuDuongThanCong.com A Heuristic for Minimum-Width Graph Layering 575 contains a number of unspecified parameters We specify them later in Section by extensive parameter study We employ two variables widthCurrent and widthUp which are used to store the width of the current layer and the width of the layers above it respectively The width of the current layer, widthCurrent, is calculated as the sum of the widths of the nodes already placed in that layer plus the sum of the widths of the potential dummy nodes along edges with a source in V \ U and a target in Z (one dummy node per edge) The variable widthUp provides an estimation of the width of any layer above the current one It is the sum of the widths of the potential dummy nodes along edges with a source in V \ U and a target in U (one dummy node per edge) When we select a node to be placed in a layer we employ an additional condition ConditionSelect Our intention is to specify ConditionSelect so that the choice of node (among alternative candidates) will lead to as narrow a layering as possible We propose to explore the following three alternatives as ConditionSelect: is the candidate with the maximum outdegree is the candidate with the maximum or any immediate predecessor of has the maximum among all candidates and their immediate predecessors In we select the candidate with the maximum indegree because that choice will lead to the maximum possible improvement of widthCurrent and are less greedy alternatives which not make the best choice in terms of widthCurrent but look also at the effect to the upper layers By choosing the CuuDuongThanCong.com 576 A Tarassov, N.S Nikolov, and J Branke candidate with the maximum makes the choice that will bring the best improvement to widthUp The idea behind is to allow nodes which can bring big improvement to the width of some upper layer to it without being blocked by their successors with low Thus, represents an alternative that tries to choose a node by looking ahead at the impact of that choice to the layering width In order to control the width of the layering we introduce a second modification to the longest-path algorithm That is, we introduce an additional condition for moving up to a new layer, ConditionGoUp The idea is to move to a new layer if the width of the current layer or of the layer above it becomes too large In order to be able to check this we introduce the parameter UBW against which we would like to compare the width of the current layer Since widthUp represents only an approximation of the width of the layers above the current layer we propose to compare its width to where i.e gives freedom to widthUp to be larger than widthCurrent because widthUp is just an estimation of the width of the upper layers We not consider UBW and as input parameters, we would like to have their values (or narrow value ranges) hard-coded in MinWidth instead We set up ConditionGoUp to be satisfied if either: widthCurrent widthUp UBW and or We require for widthCurrent UBW to be taken into account because the initial value of widthCurrent is determined by the dummy nodes in the current layer and it gets smaller (or at least it does not change) when a regular node with a positive outdegree gets placed in the current layer In that case the dummy nodes along edges with a source are removed from the current layer and get replaced by If then the condition widthCurrent UBW on its own is not a reason for moving to the upper layer because there is still a chance to add nodes to the current layer which will reduce widthCurrent If then the assignment of to the current layer increases widthCurrent because it does not replace any dummy nodes This is an indication that no further improvement of widthCurrent can be done In relation to the three alternatives, and we consider two alternative modes of updating the value of widthUp: Set widthUp at when move to the upper layer; add to widthUp each time a node is assigned to the current layer; Do not change widthUp when move to the upper layer; add to widthUp each time a node is assigned to the current layer The first of the two modes builds up widthUp starting from zero and taking into account only dummy nodes along edges between V\U and the current layer We employ this update mode with The second mode approximates the width of the upper layers more precisely by keeping track of as many dummy nodes as possible We employ it with and where the width of the upper layers CuuDuongThanCong.com A Heuristic for Minimum-Width Graph Layering 577 plays more important role We consider the three alternatives and with the corresponding widthUp update modes as parallel branches in the rough version of MinWidth and we choose one of them as a result of our experimental work In order to specify ConditionGoUp we need to set UBW and To specify ConditionSelect we need to select one of and We propose to run MinWidth for 5911 test DAGs and various sets of values of UBW and as well as for each of the alternatives or with the corresponding widthUp update mode We expect that the extensive experiments will suggest the most appropriate values or ranges of values for UBW and as well as the winner among the alternatives Parameter Study In our experimental work we used 5911 DAGs from the well-known Rome graph dataset [5] The Rome graphs come from practical applications They are graphs with node count between 10 and 100 nodes and typically each of them has twice as many edges as nodes We run MinWidth with each of the three alternatives and for each of the 5911 DAGs and for each pair (UBW, with UBW = 50, and In total, we had about million tasks We executed the tasks in a computational grid environment with two computational nodes One of the computational nodes was a PC with a Pentium III/800 MHz processor, and the other was a PC with a Pentium 4/2.4 GHz processor 4.1 and Compared For each of the 5911 input DAGs and each alternative and - we chose the layering with the smallest width (taking into account the dummy nodes) and stored the pair of parameters (UBW, for which it was achieved As we stated above, we explored any combination of UBW with = 50, and Figures 3-8 compare various properties of the stored layerings The in all pictures represents the number of original nodes in a graph Since the Rome graphs have no node labels we assume that the width of all original and all dummy nodes is unit if not specified otherwise Thus, the layering width is the maximum number of nodes (original and dummy) per layer We have partitioned all DAGs into groups by node count Each group covers an interval of size on the We display the average result for each group Figures (a) and (b) compare the width of the layerings taking into account the dummy nodes (i.e each dummy node has width equal to one unit) and neglecting them (i.e each dummy node has width equal to zero) respectively In both cases gives the narrowest layerings which suggests that might be the best option if the width of the dummy nodes is considered less than or equal to one unit (which is a reasonable assumption) The height of the layerings (see Figure 4) is larger than the height of the other layerings The height is the number of layers It was expected that the narrower a layering, the larger is the CuuDuongThanCong.com 578 A Tarassov, N.S Nikolov, and J Branke Fig and compared: layering width (a) taking into account and (b) neglecting the contribution of the dummy nodes Fig and compared: layering height (number of layers) number layers Figure 5(a) shows the dummy node count divided by the total node count in a DAG Figure 5(b) shows the edge density divided by the total edge count in a DAG We can observe that the layerings have fewer dummy nodes and in general better edge density than the and the layerings Similarly, Figures 6(a) and (b) show the values of UBW and which lead to narrowest layerings The simplest alternative finds narrowest layerings for considerably lower values of UBW and than and Moreover, those values of UBW and not depend on the DAG size when is employed The conclusion that we can make from these experiments is that the simplest alternative, is superior to the other two It is enough to run MinWidth with UBW = and in order to achieve the narrowest possible layerings In any case MinWidth leads to layerings with a very high dummy node count There is a simple heuristic that can be applied to a layering in order to reduce the dummy node count It is the Promotion heuristic which works by iteratively moving (or promoting) nodes to upper layers if that movement decreases CuuDuongThanCong.com A Heuristic for Minimum-Width Graph Layering Fig and (b) the edge density Fig and layering was found 579 compared: normalized values of (a) the dummy node count and compared: values of (a) UBW and (b) for which a narrowest the dummy node count [9] The Promotion heuristic leads to close to the minimum dummy node count when applied to longest-path layerings Since MinWidth is based on the longest-path algorithm we expected that the same Promotion heuristic might be successfully applied to MinWidth layerings as well In the next section we compare MinWidth with followed by the Promotion heuristic to some well-known layering algorithms 4.2 Effect of Promotion Figures 6(a) and (b) suggest that when is employed it is enough to consider UBW = and Since MinWidth is very fast with fixed UBW and we can afford running it for relatively narrow ranges of UBW and values for better quality results Thus, in a new series of experiments we run MinWidth with CuuDuongThanCong.com 580 A Tarassov, N.S Nikolov, and J Branke for UBW = and and choose the combination (UBW, that leads to the narrowest layering For convenience, we call the layering achieved by this method simply MinWidth layering in the remainder of this section We post-processed MinWidth layerings by applying to them the Promotion heuristic modified to perform a node promotion only if it does not increase the width of the layering We also run the longest-path algorithm and the Coffman-Graham algorithm followed by the same width-preserving node promotion The Coffman-Graham algorithm takes an upper bound on the number of nodes in a layer as an input parameter [4] Thus, we run it for where is the number of nodes in the DAG, and chose the narrowest layering We also run the network simplex algorithm of Gansner et al [7] and compared the aesthetic properties of the four layering types: MinWidth, longest-path, Coffman-Graham and Gansner’s network simplex The results of the comparison are presented in Figures 7-10 Fig Effect of promotion: layering width (a) taking into account and (b) neglecting the contribution of the dummy nodes It can be observed that the promotion heuristic is very efficient when applied after MinWidth MinWidth leads to considerably narrower but taller layerings than the other three algorithms (see Figures 7(a) and (b)) It was expected that the narrower a layering, the larger is the number of layers This can be confirmed in Figure 10(a) The number of dummy nodes in the MinWidth layerings is close to the number of dummy nodes in the Coffman-Graham layerings and slightly higher than the number of dummy nodes in the longest-path and Gansner’s layerings as it can be seen in Figure 8(a) However, Figure 8(b) shows that the MinWidth layerings have considerably lower edge density than the other layerings which means that they could possibly lead to clean drawings with small number of edge crossings The number of edge crossings is widely accepted as one of the most important graph drawing aesthetic criteria [10] CuuDuongThanCong.com A Heuristic for Minimum-Width Graph Layering 581 Fig Effect of promotion: normalized values of (a) the dummy node count and (b) the edge density Fig Two layerings of the same DAG The MinWidth layering is narrower than the Gansner’s layering (assuming all DAG nodes and all dummy nodes have width one unit) All edges point downwards Figure shows an example of the MinWidth layering of a DAG compared to the Gansner’s layering of the same DAG The DAG is taken from the Rome’s graph dataset We run the second group of experiments on a single Pentium 4/2.4 GHz processor The running times are presented in Figure 10(b) We observed that the average running time for MinWidth followed by promotion is up to seconds for DAGs having no more than 75 nodes and it grows up to 6.2 seconds for DAGs with more than 75 and less than 100 nodes The total running time CuuDuongThanCong.com 582 A Tarassov, N.S Nikolov, and J Branke for the Coffman-Graham algorithm was within seconds and the longest-path algorithms was the fastest of the three with running time within seconds The Gansner’s layerings (which we computed with ILOG CPLEX) are the fastest to be computed Fig 10 Effect of promotion: (a) layering height and (b) running times in seconds Conclusions Our parameter study shows that MinWidth with UBW = 4, and followed by width-preserving node promotion can be successfully employed as a heuristic for layering with the minimum width taking into account the contribution of the dummy nodes This is the first successful attempt to design a heuristic for the NP-hard problem of minimum-width DAG layering with consideration of dummy nodes It does not guarantee the minimum width but performs significantly faster than the only other alternative which is the exponential-time branch-and-cut algorithm of Healy and Nikolov The aesthetic properties of the MinWidth layerings compare well to the properties of the layerings constructed by the well-known layering algorithms The MinWidth layerings have the lowest edge density which suggests that they could lead to clear and easy to comprehend drawings in the context of the STT method for hierarchical graph drawing It has to be noted that the promotion heuristic slows down the computation significantly but the running time is still very acceptable for DAGs with up to 100 nodes The work we present can be continued by exploring other possibilities for the conditions we set up in MinWidth However, we believe that MinWidth finds layerings which are narrow enough for practical applications Further research could be related to the optimization of the running time of MinWidth and to experiments with larger DAGs and with DAGs with variable node widths CuuDuongThanCong.com A Heuristic for Minimum-Width Graph Layering 583 References J Branke, P Eades, S Leppert, and M Middendorf Width restricted layering of acyclic digraphs with consideration of dummy nodes Technical Report No 403, Intitute AIFB, University of Karlsruhe, 76128 Karlsruhe, Germany, 2001 J Branke, S Leppert, M Middendorf, and P Eades Width-restriced layering of acyclic digraphs with consideration of dummy nodes Information Processing Letters, 81(2):59–63, January 2002 M J Carpano Automatic display of hierarchized graphs for computer aided decision analysis IEEE Transactions on Systems, Man and Cybernetics, 10(11):705– 715, 1980 E G Coffman and R L Graham Optimal scheduling for two processor systems Acta Informatica, 1:200–213, 1972 G Di Battista, A Garg, G Liotta, R Tamassia, E Tassinari, and F Vargiu An experimental comparison of four graph drawing algorithms Computational Geometry: Theory and Applications, 7:303–316, 1997 P Eades, X Lin, and W F Smyth A fast and effective heuristic for the feedback arc set problem Information Processing Letters, 47:319–323, 1993 E R Gansner, E Koutsofios, S C North, and K.-P Vo A technique for drawing directed graphs IEEE Transactions on Software Engineering, 19(3):214–230, March 1993 P Healy and N S Nikolov A branch-and-cut approach to the directed acyclic graph layering problem In M Goodrich and S Koburov, editors, Graph Drawing: Proceedings of 10th International Symposium, GD 2002, volume 2528 of Lecture Notes in Computer Science, pages 98–109 Springer-Verlag, 2002 N.S Nikolov and A Tarassov Graph layering by promotion of nodes Special issue of Discrete Applied Mathematics associated with the IV ALIO/EURO Workshop on Applied Combinatorial Optimization, to appear 10 H C Purchase, R F Cohen, and M James Validating graph drawing aesthetics In F J Brandenburg, editor, Graph Drawing: Symposium on Graph Drawing, GD ‘95, volume 1027 of Lecture Notes in Computer Science, pages 435–446 SpringerVerlag, 1996 11 K Sugiyama and K Misue Graph drawing by the magneting spring model Journal of Visual Languages and Computing, 6(3):217–231, 1995 12 K Sugiyama, S Tagawa, and M Toda Methods for visual understanding of hierarchical system structures IEEE Transaction on Systems, Man, and Cybernetics, 11(2):109–125, February 1981 13 J Utech, J Branke, H Schmeck, and P Eades An evolutionary algorithm for drawing directed graphs In Proceedings of the 1998 International Conference on Imaging Science, Systems, and Technology (CISST’98), pages 154–160, 1998 14 J N Warfield Crossing theory and hierarchy mapping IEEE Transactions on Systems, Man and Cybernetics, 7(7):502–523, 1977 CuuDuongThanCong.com This page intentionally left blank CuuDuongThanCong.com Author Index Alvim, Adriana C.F Amaldi, Edoardo 14 Araujo, Guido 545 Aringhieri, Roberto 30 Ballester, Pedro J 42 Bartodziej, Paul 57 Basseur, Matthieu 72 Bloch, Isabelle 100 Bodlaender, Hans L 87 Boeres, Maria C 100 Boros, Endre 114 Boyer, John M 129 Bracht, Evandro C 145 Branke, Jürgen 570 Carter, Jonathan N 42 Chatzigiannakis, Ioannis 159 Cintra, Glauber 175 Cruz, Laura 417 Demetrescu, Camil 191 Derigs, Ulrich 57 Dhaenens, Clarisse 72 Dimitriou, Tassos 199 Du, Jingde 213 Duch, Amalia 228 Elbassioni, Khaled 114 Fernandes, Cristina G 129 Figueiredo, Celina M.H de 87, 243 Fonseca, Guilherme D da 243 Frausto, Juan 417 Fredriksson, Kimmo 285 García-Nocetti, Fabián 369 Gurvich, Vladimir 114 Gutierrez, Marisa 87 Hanashiro, Erik J 253 Holzer, Martin 269 Hyyrö, Heikki 285 Italiano, Giuseppe F Jo, Junha 301 CuuDuongThanCong.com 191 Karp, Richard M 299 Kelly, Paul H.J 383 Khachiyan, Leonid 114 Kim, Dong K 301 Kloks, Ton 87 Kolliopoulos, Stavros G 213 Lemesre, Julien 72 Liberti, Leo 14 Lima, André M 545 Lucena, Abílio 458 Lucet, Corinne 315 Maculan, Nelson 14 Maffioli, Francesco 14 Markou, Michael 159 Martínez, Conrado 228, 326 Martinhon, Carlos A 341 Martins, Simone L 498 Meira, Luis A.A 145 Mendes, Florence 315 Miyazawa, Flávio K 145 Molinero, Xavier 326 Mongelli, Henrique 253 Moreano, Nahri 545 Moukrim, Aziz 315 Navarro, Gonzalo Niedermeier, Rolf Nikoletseas, Sotiris Nikolov, Nikola S Noma, Alexandre 285 87 159 570 129 Ochi, Luiz S 468, 498 Oliveira, Carlos A.S 356 Ovalle-Martínez, Francisco Javier Pardalos, Panos M 356 Park, Heejin 301 Pazos, Rodolfo A 417 Pearce, David J 383 Pemmaraju, Sriram V 399 Penumatcha, Sriram 399 Pérez, Joaquín 417 Phan, Vinhthuy 432 369 586 Author Index Pina, José C de 129 Pinto, Paulo E.D 446 Protti, Fábio 341,446 Raman, Rajiv 399 Resende, Mauricio G.C 356 Ribeiro, Celso C 1,100, 458 Rodríguez, Guillermo 417 Rolim, Jose 559 Romero, David 417 Sá, Vinícius G.P de 243 Santos, Andréa C dos 458 Santos, Haroldo G 468 Sawitzki, Daniel 482 Schulz, Frank 269 Silva, Geiza C 498 Sinha, Ranjan 513, 529 CuuDuongThanCong.com Skiena, Steven 432 Solano-González, Julio 369 Song, Siang W 253 Souza, Cid C 545 Souza, Marcone J.F 468 Spinrad, Jeremy 243 Spirakis, Paul 199 Stojmenovic, Ivan 369 Szwarcfiter, Jayme L 446 Tadonki, Claude 559 Talbi, El-Ghazali 72 Tarassov, Alexandre 570 Wakabayashi, Yoshiko 175 Willhalm, Thomas 269 Zobel, Justin 529 CuuDuongThanCong.com ... e-mail: maculan@cos.ufrj.br C.C Ribeiro and S.L Martins (Eds.): WEA 2004, LNCS 3059 , pp 14–29, 2004 © Springer-Verlag Berlin Heidelberg 2004 CuuDuongThanCong.com Efficient Edge-Swapping Heuristics... of instance I and H(I) is the makespan of the solution computed by heuristic H The longest processing time (LPT) C.C Ribeiro and S.L Martins (Eds.): WEA 2004, LNCS 3059 , pp 1–13, 2004 © Springer-Verlag... Lenstra, A.H.G Rinnooy Kan, and D.B Shmoys, “Sequencing and scheduling: Algorithms and complexity”, in Logistics of Production and Inventory: Handbooks in Operations Research and Management Science