ISSN 004-8917 AUSTRALIAN JOURNAL Volume 24, Number 2, May 1992 SPECIAL ISSUE ON ALGORITHMS 41 Guest Editorial 42 Algorithmic Issues in the Geometry of Planar Linkage Movement S WHITESIDES 51 Algorithms for Groups J CANNON and GEORGE HA VAS 61 Parallel Search Algorithms for Trees and Graphs PCHAUDHUR1 70 An Overview of Adaptive Sorting A MOFFA T and O PETERSSON SPECIAL FEATURES 50 Book Review Information 78 Book Reviews Published for Australian Computer Society Incorporated Registered by Australia Post, Publication No. NBG 1124 AUSTRALIAN Editor Computer R COOK, The University of Queensland ———■«™——«■—— iiiiiiiiii iiiiiiiiiiii Editorial Co-ordinator LOIS FORDHAM, The University of 77ie Australian Computer Journal is an official publication Queensland of the Australian Computer Society Incorporated. Associate Editors CONTRIBUTIONS to ensure uniformity of style. 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The search for a good of the research. sorting algorithm began as soon as the first machines were The first paper falls within the subfield of computa­ powered up; today, a section on sorting is an integral part tional geometry, an area which has been very active over of every computer science curriculum. Many proposals for the last few years. Its popularity is driven by the increasing adaptive sorting algorithms have been made in the last 10 number of computational problems with a geometric fla­ years; these are algorithms which sort a list faster if the list vour: in Robotics, Geographical Information Systems, is already “partially sorted”. Moffat and Petersson discuss Graphics and Visualisation. Whitesides presents the com­ the competing formal notions of “partially sorted” and putational geometry approach to motion planning for lin­ give an introduction to algorithms which exploit this kages in a restricted environment. “presortedness”. There has always been a strong collaboration between mathematicians and computer scientists working in algo­ REFERENCE rithms. In the past, the main flow of ideas has been for 1 Les Goldschlager and Andrew Lister, Computer Science, A Modem mathematics to computer science. The second paper, by Introduction, Prentice Hall International Series in Computer Science, 2nd edition 1988, page xi. Cannon and Havas shows, that the flow has become bidi­ rectional. The paper surveys algorithmic methods which have been successful in group theory, one of the fundamen­ Peter Eades Alistair Moffat tal branches of algebra. Professor and Head Senior Lecturer Algorithms research has often focused on improving of Computer Science Department of Computer the resource efficiency of computation. It is clear that for The University of Science many problems, future improvements in time efficiency Newcastle The University of can only be achieved with massive parallelism. The third Melbourne i THE AUSTRALIAN COMPUTER JOURNAL, VOL. 24, No. 2, MAY 1992 41 1 INTRODUCTION Algorithmic Issues This paper considers the planning of planar placements and motions for linkages, especially chains of links. A linkage consists of a collection of rigid rods of given in the Geometry of lengths. Rods may be fastened together at their endpoints, which act like planar universal joints. When the linkage is placed in the plane, its rods are allowed to cross over one Planar Linkage another. As the linkage moves, the rods may rotate freely about their endpoints, subject only to the constraint that Movement distances between certain joints are determined by the existence of rods between them. Sue