As graph models are applied to more widely varying fields, researchers struggle with tools for exploring and analyzing these structures. We describe GUESS, a novel system for graph exploration that combines an interpreted language with a graphical front end that allows researchers to rapidly prototype and deploy new visualizations. GUESS also contains a novel, interactive interpreter that connects the language and interface in a way that facilities exploratory visualization tasks. Our language, Gython, is a domain-specific embedded language which provides all the advantages of Python with new, graph specific operators, primitives, and shortcuts. We highlight key aspects of the system in the context of a large user survey and specific, real-world, case studies ranging from social and knowledge networks to distributed computer network analysis.

this paper has been supported in part by ESPRIT IV LTR Projects No. 21957 (CGAL) and No. 28155 (GALIA), by the USA-Israel Binational Science Foundation, by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Center for Geometric Computing and its Applications), by a Franco-Israeli research grant "factory of the future" (monitored by AFIRST/France and The Israeli Ministry of Science), and by the Hermann Minkowski -- Minerva Center for Geometry at Tel Aviv University

Several algorithms for computing the Minkowski sum of two polygons in the plane begin by decomposing each polygon into convex subpolygons. We examine different methods for decomposing polygons by their suitability for efficient construction of Minkowski sums. We study and experiment with various well-known decompositions as well as with several new decomposition schemes. We report on our experiments with various decompositions and different input polygons. Among our findings are that in general: (i) triangulations are too costly (ii) what constitutes a good decomposition for one of the input polygons depends on the other input polygon --- consequently, we develop a procedure for simultaneously decomposing the two polygons such that a "mixed" objective function is minimized, (iii) there are optimal decomposition algorithms that significantly expedite the Minkowski-sum computation, but the decomposition itself is expensive to compute --- in such cases simple heuristics that approximate the optimal decomposition perform very well.

A phylogeny is the evolutionary history of a group of organisms; systematists (and other biologists) attempt to reconstruct this history from various forms of data about contemporary organisms. Phylogeny reconstruction is a crucial step in the understanding of evolution as well as an important tool in biological, pharmaceutical, and medical research. Phylogeny reconstruction from molecular data is very difficult: almost all optimization models give rise to NP-hard (and thus computationally intractable) problems. Yet approximations must be of very high quality in order to avoid outright biological nonsense. Thus many biologists have been willing to run farms of processors for many months in order to analyze just one dataset. High-performance algorithm engineering offers a battery of tools that can reduce, sometimes spectacularly, the running time of existing phylogenetic algorithms, as well as help designers produce better algorithms. We present an overview of algorithm engineering techniques, illustrating them with an application to the "breakpoint analysis" method of Sankoff et al., which resulted in the GRAPPA software suite. GRAPPA demonstrated a speedup in running time by over eight orders of magnitude over the original implementation on a variety of real and simulated datasets. We show how these algorithmic engineering techniques are directly applicable to a large variety of challenging combinatorial problems in computational biology.

The Minkowski sum (also known as the vector sum) of two sets P and Q in IR 2 is the set fp + q j p 2 P; q 2 Qg. Minkowski sums are useful in robot motion planning, computer-aided design and manufacturing (CAD/CAM) and many other areas. We present a software package for robust and efficient construction of Minkowski sums of planar polygonal sets. We describe the different algorithms that we implemented and an experimental comparison between them. A distinctive feature of our implementation is that it can accurately handle degenerate input and in particular it can identify degenerate "holes" in the

In this paper we discuss the gap between the theory and practice of geometric algorithms. We then describe effors to settle this gap and facilitate the successful implementation of geometric algorithms in general and of algorithms for geometric arrangements and motion planning in particular.

. Given a collection C of curves in the plane, the arrangement of C is the subdivision of the plane into vertices, edges and faces induced by the curves in C. Constructing arrangements of curves in the plane is a basic problem in computational geometry. Applications relying on arrangements arise in fields such as robotics, computer vision and computer graphics. Many algorithms for constructing and maintaining arrangements under various conditions have been published in papers. However, there are not many implementations of (general) arrangements packages available. We present an implementation of a generic and robust package for arrangements of curves that is part of the CGAL 1 library. We also present an application based on this package for adaptive point location in arrangements of parametric curves. 1

Contents Acknowledgments iii 1 Introduction 3 2 Preliminaries and Related Work 9 2.1 CGAL and Generic Programming . . . . . . . . . . . . . . . . 9 2.2 Robustness in Geometric Computation . . . . . . . . . . . . . 11 2.2.1 Exact Arithmetic . . . . . . . . . . . . . . . . . . . . . 12 2.2.2 Floating Point Filters . . . . . . . . . . . . . . . . . . . 13 2.3 Planar Maps in CGAL . . . . . . . . . . . . . . . . . . . . . . 16 2.3.1 Geometric Traits . . . . . . . . . . . . . . . . . . . . . 16 2.3.2 Point Location Strategies . . . . . . . . . . . . . . . . . 17 2.4 Computing the Combinatorial Structure of an Arrangement . 18 2.4.1 Conditions for Curves . . . . . . . . . . . . . . . . . . 18 2.4.2 Isolation of Intersection Points . . . . . . . . . . . . . . 21 3 Arrangements in CGAL 23 3.1 Hierarchy Tree . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2 Design and Implementation Details . . . . . . . . . . . . . . . 26 3.2.1 General Design . . . . . . .

The last twenty years have seen enormous progress in the design of algorithms, but little of it has been put into practice. Because many recently developed algorithms are hard to characterize theoretically and have large running-time coefficients, the gap between theory and practice has widened over these years. Experimentation is indispensable in the assessment of heuristics for hard problems, in the characterization of asymptotic behavior of complex algorithms, and in the comparison of competing designs for tractable problems. Implementation, although perhaps not rigorous experimentation, was characteristic of early work in algorithms and data structures. Donald Knuth has throughout insisted on testing every algorithm and conducting analyses that can predict behavior on actual data; more recently, Jon Bentley has vividly illustrated the difficulty of implementation and the value of testing. Numerical analysts have long understood the need for standardized test suites to ensure robustness, precision and efficiency of numerical libraries. It is only recently, however, that the algorithms community has shown signs of returning to implementation and testing as an integral part of algorithm development. The emerging disciplines of experimental algorithmics and algorithm engineering have revived and are extending many of the approaches used by computing pioneers such as Floyd and Knuth and are placing on a formal basis many of Bentley's observations. We reflect on these issues, looking back at the last thirty years of algorithm development and forward to new challenges: designing cache-aware algorithms, algorithms for mixed models of computation, algorithms for external memory, and algorithms for scientific research.

This paper describes an NP-hard combinatorial optimization problem arising in the Sloan