1

March 2015
Discrete & Computational Geometry: Volume 53 Issue 2, March 2015

**Publisher:** Springer-Verlag New York, Inc.

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.

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.

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

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

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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.

7

June 2012
Discrete & Computational Geometry: Volume 47 Issue 4, June 2012

**Publisher:** Springer-Verlag New York, Inc.

8

September 2011
ESA'11: Proceedings of the 19th European conference on Algorithms

**Publisher:** Springer-Verlag

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.

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.

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

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

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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

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.

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

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.

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

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

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

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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

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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 ...