David G Kirkpatrick Authors: Add personal information
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Bibliometrics: Citation Count: 0 We consider a generalization of the familiar art gallery problem in which individual points within the gallery need to be visible to some specified, but not necessarily uniform, number of guards. We provide an $$O(\lg \lg {\mathrm {OPT}})$$O(lglgOPT)-approximation algorithm for this multi-guarding problem in simply-connected polygonal regions, with a minimum ... Keywords: Polygon guarding, Approximation algorithm, Art gallery problem, Epsilon-net 2 December 2014 Theoretical Computer Science: Volume 553 Issue C, October, 2014 Publisher: Elsevier Science Publishers Ltd. Bibliometrics: Citation Count: 0 Let G be a graph with zero or more colours assigned to its vertices, and let v s and v t be two vertices of G. The minimum-colour path problem is to determine the minimum over all v s - v t paths of the number of colours used, where ... Keywords: Resilience, Minimum colour path problems in graphs, Wireless sensor networks, Barrier coverage 3 May 2014 Theory of Computing Systems: Volume 54 Issue 4, May 2014 Publisher: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 0 At the heart of the ideas of the work of Dutch graphic artist M.C. Escher is the idea of automation; we consider a problem that was inspired by some of his earlier and lesser known work. Specifically, a motif fragment is a connected region contained in a closed unit square. ... Keywords: Escher, Optimization, Periodicity, Ribbon patterns, Geometric structure, Tiling 4 August 2013 WADS'13: Proceedings of the 13th international conference on Algorithms and Data Structures Publisher: Springer-Verlag Bibliometrics: Citation Count: 1 This paper addresses two versions of a fundamental problem, referred to as the All-Nearest-Larger-Neighbors (ANLN) problem, defined as follows: given a one-dimensional array A of n real-valued keys, find, for each array element A [ i ], the index of a nearest array element, if one exists, whose key is ... 5 June 2013 SoCG '13: Proceedings of the twenty-ninth annual symposium on Computational geometry Publisher: ACM Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 0,   Downloads (12 Months): 5,   Downloads (Overall): 76 Full text available: PDF We study the problem of maintaining the locations of a collection of n entities that are moving with some fixed upper bound on their speed. We assume a setting where we may query the current location of entities, but handling this query takes a certain unit of time, during which ... Keywords: competitive analysis, kinetic data, input imprecision 6 July 2012 Computational Geometry: Theory and Applications: Volume 45 Issue 5-6, July, 2012 Publisher: Elsevier Science Publishers B. V. Bibliometrics: Citation Count: 0 7 June 2012 Discrete & Computational Geometry: Volume 47 Issue 4, June 2012 Publisher: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 0 8 September 2011 ESA'11: Proceedings of the 19th European conference on Algorithms Publisher: Springer-Verlag Bibliometrics: Citation Count: 0 Nearest Neighbor Searching, i.e. determining from a set S of n sites in the plane the one that is closest to a given query point q , is a classical problem in computational geometry. Fast theoretical solutions are known, e.g. point location in the Voronoi Diagram of S , or ... 9 September 2011 Discrete & Computational Geometry: Volume 46 Issue 2, September 2011 Publisher: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 7 We provide an O (log log  opt )-approximation algorithm for the problem of guarding a simple polygon with guards on the perimeter. We first design a polynomial-time algorithm for building ε -nets of size $O(\frac{1}{\varepsilon}\log\log\frac{1}{\varepsilon})$ for the instances of Hitting Set associated with our guarding problem. We then apply the technique ... Keywords: Approximation algorithm, Epsilon-nets, Perimeter guards, Polygon guarding, Vertex guards 10 September 2011 Discrete & Computational Geometry: Volume 46 Issue 2, September 2011 Publisher: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 0 We provide an O(logźlogźopt)-approximation algorithm for the problem of guarding a simple polygon with guards on the perimeter. We first design a polynomial-time algorithm for building ź-nets of size $O(\frac{1}{\varepsilon}\log\log\frac{1}{\varepsilon})$ for the instances of Hitting Set associated with our guarding problem. We then apply the technique of Brönnimann and Goodrich ... Keywords: Polygon guarding, Vertex guards, Approximation algorithm, Art gallery problem, Epsilon-nets, Perimeter guards 11 August 2011 WADS'11: Proceedings of the 12th international conference on Algorithms and data structures Publisher: Springer-Verlag Bibliometrics: Citation Count: 0 We consider the problem of searching for one of possibly many goals situated at unknown nodes in an unknown tree τ. We formulate a universal search strategy and analyse the competitiveness of its average (over all presentations of τ) total search cost with respect to strategies that are informed concerning ... 12 January 2010 Wireless Networks: Volume 16 Issue 1, January 2010 Publisher: Kluwer Academic Publishers Bibliometrics: Citation Count: 6 Downloads (6 Weeks): 0,   Downloads (12 Months): 10,   Downloads (Overall): 163 Full text available: Pdf We study the problem of routing in three-dimensional ad hoc networks. We are interested in routing algorithms that guarantee delivery and are k -local, i.e., each intermediate node v 's routing decision only depends on knowledge of the labels of the source and destination nodes, of the subgraph induced by ... Keywords: Distributed algorithms, Quasi unit disc graph, Routing, Ad hoc networks, Unit ball graph 13 December 2009 Algorithmic Aspects of Wireless Sensor Networks: 5th International Workshop, ALGOSENSORS 2009, Rhodes, Greece, July 10-11, 2009. Revised Selected Papers Publisher: Springer-Verlag Bibliometrics: Citation Count: 6 Barrier coverage in a sensor network has the goal of ensuring that all paths through the surveillance domain joining points in some start region S to some target region T will intersect the coverage region associated with at least one sensor. In this paper, we revisit a notion of redundant ... 14 September 2009 Discrete Mathematics: Volume 309 Issue 18, September, 2009 Publisher: Elsevier Science Publishers B. V. Bibliometrics: Citation Count: 0 A sequence of non-negative integers is graphical if it is the degree sequence of some graph, that is, there exists a graph G on n vertices whose ith vertex has degree d"i, for [email protected][email protected]?n. The notion of a graphical sequence has a natural reformulation and generalization in terms of ... Keywords: Certifying algorithm, Graph factor, Degree sequence, Graphical sequence, f-factor, (g,f)-factor 15 September 2009 Efficient Algorithms: Essays Dedicated to Kurt Mehlhorn on the Occasion of His 60th Birthday Publisher: Springer-Verlag Bibliometrics: Citation Count: 4 Designing and analysing efficient algorithms is important in practical applications, but it is also fun and frequently instructive, even for simple problems with no immediate applications. In this self-contained paper we try to convey some of fun of algorithm design and analysis. Hopefully, the reader will find the discussion instructive ... 16 July 2009 Computational Geometry: Theory and Applications: Volume 42 Issue 5, July, 2009 Publisher: Elsevier Science Publishers B. V. Bibliometrics: Citation Count: 3 Given a nonempty and finite multiset of points P in R^d, the Euclidean median of P, denoted M(P), is a point in R^d that minimizes the sum of the Euclidean (@?"2) distances from M(P) to the points of P. In two or more dimensions, the Euclidean median (otherwise known as ... Keywords: Approximation, Mobile clients, Weber point, Bounded velocity, Continuity, Projection, Stability, Facility location, Median 17 December 2008 ISAAC '08: Proceedings of the 19th International Symposium on Algorithms and Computation Publisher: Springer-Verlag Bibliometrics: Citation Count: 2 We address the problem of finding a polynomial-time approximation scheme for shortest bounded-curvature paths in the presence of obstacles. Given an arbitrary environment $\mathcal{E}$ consisting of polygonal obstacles, two feasible configurations, a length ℓ , and an approximation factor ε , our algorithm either (i) verifies that every feasible bounded-curvature ... 18 January 2008 ICDCN'08: Proceedings of the 9th international conference on Distributed computing and networking Publisher: Springer-Verlag Bibliometrics: Citation Count: 22 We study routing algorithms for three-dimensional ad hoc networks that guarantee delivery and are k -local, i.e., each intermediate node υ's routing decision only depends on knowledge of the labels of the source and destination nodes, of the subgraph induced by nodes within distance k of υ, and of the ... 19 June 2007 SCG '07: Proceedings of the twenty-third annual symposium on Computational geometry Publisher: ACM Bibliometrics: Citation Count: 3 Downloads (6 Weeks): 1,   Downloads (12 Months): 10,   Downloads (Overall): 340 Full text available: PDF We describe an algorithm to find a unit-curvature path between specified configurations in an arbitrary polygonal domain. Whenever such a path exists, the algorithm returns an explicit description of one such path in time that is polynomial in n (the number of features of the domain), m (the precision of ... Keywords: motion planning, path feasibility, bounded-curvature 20 January 2007 SODA '07: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 2 Downloads (6 Weeks): 1,   Downloads (12 Months): 8,   Downloads (Overall): 175 Full text available: PDF Video-on-demand broadcast protocols are commonly used to deliver video content to a large uncoordinated set of consumers. Since broadcast protocols are not attuned to individual user requests, some delay in service is unavoidable. The worst-case delay, expressed as a function of the available bandwidth, has been well studied; matching upper ...