Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer graphics, computer-aided design, robotics, pattern recognition, and operations research—give rise to problems that inherently are geometrical. This is one reason computational geometry has attracted enormous research interest in the past decade and is a well-established area today. (For standard sources, we refer to the survey article by Lee and Preparata [19841 and to the textbooks by Preparata and Shames [1985] and Edelsbrunner [1987bl.) Readers familiar with the literature of computational geometry will have noticed, especially in the last few years, an increasing interest in a geometrical construct called the Voronoi diagram. This trend can also be observed in combinatorial geometry and in a considerable number of articles in natural science journals that address the Voronoi diagram under different names specific to the respective area. Given some number of points in the plane, their Voronoi diagram divides the plane according to the nearest-neighbor

Voronoi diagrams—a survey of a fundamental geometric data structure

Many auctions involve the sale of a variety of distinct assets. Examples are airport time slots, delivery routes, network routing, and furniture. Because of complementarities or substitution effects between the different assets, bidders have preferences not just for particular items but for sets of items. For this reason, economic efficiency is enhanced if bidders are allowed to bid on bundles or combinations of different assets. This paper surveys the state of knowledge about the design of combinatorial auctions and presents some new insights. Periodic updates of portions of this survey will be posted to this journal's Online Supplements web page at http://joc.pubs.informs.org/OnlineSupplements.html.

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Combinatorial Auctions: A Survey

http://compalg.inf.elte.hu/~tony/Kutatas/BinPacking/Johnson-BinPacking-NP-Column-JAlg-2002.pdf

The NP-completeness column: An ongoing guide

Given a graphG, a subgraphG' is at-spanner ofG if, for everyu,v ?V, the distance fromu tov inG' is at mostt times longer than the distance inG. In this paper we give a simple algorithm for constructing sparse spanners for arbitrary weighted graphs. We then apply this algorithm to obtain specific results for planar graphs and Euclidean graphs. We discuss the optimality of our results and present several nearly matching lower bounds.

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On sparse spanners of weighted graphs

LetS be a set ofN points in the Euclidean plane, and letd(p, q) be the Euclidean distance between pointsp andq inS. LetG(S) be a Euclidean graph based onS and letG(p, q) be the length of the shortest path inG(S) betweenp andq. We say a Euclidean graphG(S)t-approximates the complete Euclidean graph if, for everyp, q ?S, G(p, q)/d(p, q) ≤t. In this paper we present two classes of graphs which closely approximate the complete Euclidean graph. We first consider the graph of the Delaunay triangulation ofS, DT(S). We show that DT(S) (2?/(3 cos(?/6)) ? 2.42)-approximates the complete Euclidean graph. Secondly, we define?(S), the fixed-angle?-graph (a type of geometric neighbor graph) and show that?(S) ((1/cos?)(1/(1?tan?)))-approximates the complete Euclidean graph.

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Classes of graphs which approximate the complete Euclidean graph

The problem of decomposing a polygon into simpler components is of interest in fields such as computational geometry, syntactic pattern recognition, and graphics. In this paper we consider decompositions which do not introduce Steiner points. The simpler components we consider are convex polygons, spiral polygons, star-shaped polygons and monotone polygons. We apply a technique for improving the efficiency of dynamic programming algorithms in order to achieve polynomial time algorithms for the problems of decomposing a simple polygon into the minimum number of each of the component types. Using the same technique we are able to exhibit polynomial time algorithms for the problems of decomposing a simple polygon into each of the component types while minimizing the length of the internal edges used to form the decomposition. When the polygons are allowed to contain holes many of the problems become NP-hard.

J. Mark Keil

Papers

Classes of graphs which approximate the complete Euclidean graph

Decomposing a Polygon into Simpler Components

Finding Hamiltonian circuits in interval graphs

Chapter 11 – Polygon Decomposition

Domination in permutation graphs