Jan van Leeuwen

Maintenance of configurations in the plane

For a number of common configurations of points (lines) in the plane, we develop data structures in which insertions and deletions of points (or lines, respectively) can be processed rapidly, without sacrificing much of the efficiency of query answering which known static structures for these configurations attain. As a main result we establish a fully dynamic maintenance algorithm for convex hulls that can process insertions and deletions of single points in only O(log* n) steps per transaction, where n is the number of points currently in the set. The algorithm has several intriguing applications, including the fact that the “trimmed” mean of a set of n points in the plane can be determined in only O(n log2 n) steps. Likewise, efficient algorithms are obtained for dynamically maintaining the common intersection of a set of halfspaces and for dynamically maintaining the maximal elements of a set of points. The results are all derived by means of one master technique, which is applied repeatedly and which captures an appropriate notion of “decomposability” for configurations closely related to the existence of divide-and-conquer solutions.

Worst-case Analysis of Set Union Algorithms

This paper analyzes the asymptotic worst-case running time of a number of variants of the well-known method of path compression for maintaining a collection of disjoint sets under union. We show that two one-pass methods proposed by van Leeuwen and van der Weide are asymptotically optimal, whereas several other methods, including one proposed by Rein and advocated by Dijkstra, are slower than the best methods.

The World Wide Web and Databases

The World Wide Web promises to transform human society by making virtually all types of information instantly available everywhere. Two prerequisites for this promise to be realized are a universal markup language and a universal query language. The power and flexibility of XML make it the leading candidate for a universal markup language. XML provides a way to label information from diverse data sources including structured and semi-structured documents, relational databases, and object repositories. Several XML-based query languages have been proposed, each oriented toward a specific category of information. Quilt is a new proposal that attempts to unify concepts from several of these query languages, resulting in a new language that exploits the full versatility of XML. The name Quilt suggests both the way in which features from several languages were assembled to make a new query language, and the way in which Quilt queries can combine information from diverse data sources into a query result with a new structure of its own.

Theoretical Computer Science: Exploring New Frontiers of Theoretical Informatics

Breaking and fixing the Needham-Schroeder public-key protocol using FDR.- Reconciling Two Views of Cryptography.- Theory and Construction of Molecular Computers.- Theory and Construction of Molecular Computers.- On the hardness of the permanent.- List Decoding: Algorithms and Applications.- Approximation Algorithms for String Folding Problems.- Approximation Algorithms for String Folding Problems.- Fast multi-dimensional approximate string matching.- An Index for Two Dimensional String Matching Allowing Rotations.- Parallel Edge Coloring of a Tree on a Mesh Connected Computer.- Parallel Edge Coloring of a Tree on a Mesh Connected Computer.- Linear Time 1/2-Approximation Algorithm for Maximum Weighted Matching in General Graphs.- Parallel Approximation Algorithms for Maximum Weighted Matching in General Graphs.- It Is on the Boundary: Complexity Considerations for Polynomial Ideals.- It Is on the Boundary: Complexity Considerations for Polynomial Ideals.- An Efficient Parallel Algorithm for Scheduling Interval Ordered Tasks.- An Efficient Parallel Algorithm for Scheduling Interval Ordered Tasks.- Reducibility among combinatorial problems.- Task Distributions on Multiprocessor Systems.- Fast Interpolation Using Kohonen Self-Organizing Neural Networks.- Fast Interpolation Using Kohonen Self-Organizing Neural Networks.- Steganography Using Modern Arts.- Steganography Using Modern Arts.- Gossiping in Vertex-Disjoint Paths Mode in d-dimensional Grids and Planar Graphs.- Trade-Offs between Density and Robustness in Random Interconnection Graphs.- An effcient way for edge-connectivity augmentation.- The (? + 1)-Edge-Connectivity Augmentation Problem without Creating Multiple Edges of a Graph.- On the Approximability of NP-complete Optimization Problems.- On the Hardness of Approximating Some NP-Optimization Problems Related to Minimum Linear Ordering Problem.- How Many People Can Hide in a Terrain ?.- Maximum Clique and Minimum Clique Partition in Visibility Graphs.- Language recognition and the synchronization of cellular automata.- Real-Time Language Recognition by Alternating Cellular Automata.- Inducing an order on cellular automata by a grouping operation.- Damage Spreading and ?-Sensitivity on Cellular Automata.- Financial Applications of Monte Carlo and Quasi-Monte Carlo Methods.- Discrepancy Theory and Its Application to Finance.- Fully consistent extensions of partially defined Boolean functions with missing bits.- Fully Consistent Extensions of Partially Defined Boolean Functions with Missing Bitsv.- Dealing necessary and sufficient numbers of cards for sharing a one-bit secret key.- Characterization of Optimal Key Set Protocols.- Algebraic Complexity Theory.- On the Complexity of Integer Programming in the Blum-Shub-Smale Computational Model.- On Logarithmic Simulated Annealing.- On Logarithmic Simulated Annealing.- Specification and verification of concurrent programs in CESAR.- Hierarchical State Machines.- Validating firewalls in mobile ambients.- Ambient Groups and Mobility Types.- Multiway synchronization verified with coupled simulation.- An Asynchronous, Distributed Implementation of Mobile Ambients.- Graph types for monadic mobile processes.- Type Systems for Concurrent Processes: From Deadlock-Freedom to Livelock-Freedom, Time-Boundedness.- Aliasing Models for Mobile Objects.- Local ?-Calculus at Work: Mobile Objects as Mobile Processes.- Typed concurrent objects.- An Interpretation of Typed Concurrent Objects in the Blue Calculus.- Inductive definitions in the system coq. rules and properties.- A Higher-Order Specification of the ?-Calculus.- Compositionality through an operational semantics of contexts.- Open Ended Systems, Dynamic Bisimulation and Tile Logic.- Observe behaviour categorically.- Fibred Models of Processes: Discrete, Continuous, and Hybrid Systems.- The Equivalence Problem for Deterministic Pushdown Automata is Decidable.- On the Complexity of Bisimulation Problems for Pushdown Automata.- Session 2.4.- A Type-Theoretic Study on Partial Continuations.- Partially Typed Terms between Church-Style and Curry-Style.- Alternating Automata and Logics over Infinite Words.- Hypothesis Support for Information Integration in Four-Valued Logics.- Invited Talk 2.2.- Masaccio: A Formal Model for Embedded Components.- Session 2.5.- A Single Complete Refinement Rule for Demonic Specifications.- Reasoning about Composition Using Property Transformers and Their Conjugates.- Invited Talk 2.3.- Some New Directions in the Syntax and Semantics of Formal Languages.- Panel Discussion on New Challanges for TCS.- New Challenges for Theoretical Computer Science.- Algorithm Design Challenges.- Quantumization of Theoretical Informatics.- Two Problems in Wide Area Network Programming.- New Challenges for Computational Models.- Towards a Computational Theory of Everything.- Open Lectures.- On the Power of Interactive Computing.- The Varieties of Programming Language Semantics.

The measure problem for rectangular ranges in d-space☆

Klee recently posed the question: find an efficient algorithm for computing the measure of a set of n intervals on the line, and the analog for n hyperrectangles (ranges) in d-space. The one-dimensional case is easily solved in O(n log n) and Bentley has proved an O(nd−1log n) algorithm for dimension d ≥ 2. We present an algorithm for Klees measure problem that has a worst-case running time of only O(nd−1) for d⩾3. While Bentleys algorithm is based on segment trees and requires only linear storage for any dimension, the new method is based on quad-trees and requires quadratic storage for d > 2.

Viewpoint Research evaluation for computer science

Reassessing the assessment criteria and techniques traditionally used in evaluating computer science research effectiveness.

λ -Coloring of Graphs

A λ-coloring of a graph G is an assignment of colors from the set {0,....,λ} to the vertices of a graph G such that vertices at distance at most two get different colors and adjacent vertices get colors which are at least two apart. The problem of finding λ-colorings with small or optimal λ arises in the context of radio frequency assignment. We show that the problems of finding the minimum λ for planar graphs, bipartite graphs, chordal graphs and split graphs are NP-Complete. We then give approximation algorithms for λ-coloring and compute upperbounds of the best possible λ for outerplanar graphs, planar graphs, graphs of treewidth k, permutation and split graphs. With the exception of the split graphs, all the above bounds for λ are linear in Δ, the maximum degree of the graph. For split graphs, we give a bound of λ ≤1.5+2Δ+2 and show that there are split graphs with λ = Ω(Δ1.5). Similar results are also given for variations of the λ-coloring problem.

Dynamic multi-dimensional data structures based on quad- and k--d trees

SummaryQuad-trees and k—d trees have been noted for their lack of dynamic properties as data structures for multi-dimensional point sets. We describe a method to insert points in a quad-tree while keeping the tree balanced that achieves an average time complexity of O(log2 N) per insertion, where N is the number of updates performed on the quad-tree. We define a structure similar to a quad-tree, called a pseudo quad-tree, and show how it can be used to handle both insertions and deletions in O(log2N) average time. We also discuss how quad-trees and pseudo quadtrees can be extended for use in configurations of points in which more than one point may have a same value in some equal coordinate, without altering the earlier time bounds for insertions, deletions and queries. Similar algorithms are given for k—d trees and the same average time bounds for insertion and deletion are achieved.

Algorithm Theory - SWAT 2000

First we review amortized fully-dynamic polylogarithmic algorithms for connectivity, minimum spanning trees (MST), 2-edgeand biconnectivity. Second we discuss how they yield improved static algorithms: connectivity for constructing a tree from homeomorphic subtrees, 2-edge connectivity for finding unique matchings in graphs, and MST for packing spanning trees in graphs. The application of MST for spanning tree packing is new and when boot-strapped, it yields a fully-dynamic polylogarithmic algorithm for approximating general edge connectivity within a factor √ 2 + o(1). Finally, on the more practical side, we will discuss how output sensitive algorithms for dynamic shortest paths have been applied successfully to speed up local search algorithms for improving routing on the internet, roughly doubling the capacity. 1 Dynamic Graph Algorithms In this talk, we will discuss some simple dynamic graph algorithms and their applications within static graph problems. As a new result, we will derive a fully dynamic polylogarithmic algorithm approximating the edge connectivity λ within a factor √ 2 + o(1), that is, the algorithm will output a value between λ/ √ 2 + o(1) and λ ×2 + o(1). The talk is not intended as a general survey of dynamic graph algorithms and their applications. Rather its goal is just to present a few nice illustrations of the potent relationship between dynamic graph algorithms and their applications in static graph problems, showing contexts in which dynamic graph algorithms play a role similar to that played by priority queues for greedy algorithms. In a fully dynamic graph problem, we are considering a graph G over a fixed vertex set V , |V | = n. The graph G may be updated by insertions and deletions of edges. Unless otherwise stated, we assume that we start with an empty edge set. We will review the fully dynamic graph algorithms of Holm et al. [11] for connectivity, minimum spanning trees (MST), 2-edge, and biconnectivity in undirected graphs. For the connectivity type problems, the updates may be interspersed by queries on (2-edge-/bi-) connectivity of the graph or between specified vertices. For MST, the fully dynamic algorithm should update the MST in connection with each update to the graph: an inserted edge might have to go into the MST, and if an MST edge is deleted, we should replace with the lightest edge possible. M.M. Halldórsson (Ed.): SWAT 2000, LNCS 1851, pp. 1–9, 2000. c

Efficient elections in chordal ring networks

We study the message complexity of the problem of distributively electing a leader in chordal rings. Such networks consist of a basic ring with additional links, the extreme cases being the oriented ring and the complete graph with a full sense of direction. We present a general election algorithm for these networks, and prove its optimality. As a corollary, we show thatO(logn) chords at each processor suffice to obtain an algorithm that uses at mostO(n) messages; this improves and extends a previous work, where an algorithm, also usingO(n) messages, was suggested for the case where alln-1 chords exist (the oriented complete network).