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Aimed at an audience of researchers and graduate students in computational geometry and algorithm design, this book uses the Geometric Spanner Network Problem to showcase a number of useful algorithmic techniques, data structure strategies, and geometric analysis techniques with many applications, practical and theoretical. The authors present rigorous… (More)

- Kalai Mathee, Giri Narasimhan, +17 authors Stephen Lory
- Proceedings of the National Academy of Sciences…
- 2008

One of the hallmarks of the Gram-negative bacterium Pseudomonas aeruginosa is its ability to thrive in diverse environments that includes humans with a variety of debilitating diseases or immune deficiencies. Here we report the complete sequence and comparative analysis of the genomes of two representative P. aeruginosa strains isolated from cystic fibrosis… (More)

- Moses Charikar, Samir Khuller, David M. Mount, Giri Narasimhan
- SODA
- 2001

Facility location problems are traditionally investigated with the assumption that <i>all</i> the clients are to be provided service. A significant shortcoming of this formulation is that a few very distant clients, called <i>outliers</i>, can exert a disproportionately strong influence over the final solution. In this paper we explore a generalization of… (More)

- Gautam Das, Giri Narasimhan
- Int. J. Comput. Geometry Appl.
- 1994

Let <italic>G=(V,E)</italic> be a <italic>n</italic>-vertex connected graph with positive edge weights. A subgraph <italic>G</italic>′ is a <italic>t</italic>-spanner if for all <italic>u,v</italic><inline-equation> <f> ∈</f> </inline-equation><italic>V</italic>, the distance between <italic>u</italic> and <italic>v</italic> in the subgraph is… (More)

- Giri Narasimhan, Michiel H. M. Smid
- SIAM J. Comput.
- 2000

There are several results available in the literature dealing with efficient construction of t-spanners for a given set S of n points in Rd. t-spanners are Euclidean graphs in which distances between vertices in G are at most t times the Euclidean distances between them; in other words, distances in G are “stretched” by a factor of at most t. We consider… (More)

- Barun Chandra, Gautam Das, Giri Narasimhan, José Soares
- Int. J. Comput. Geometry Appl.
- 1992

Let <italic>G</italic>=(<italic>V,E</italic>) be an <italic>n</italic>-vertex connected graph with positive edge weights. A subgraph <italic>G</italic>′ = (<italic>V,E</italic>′) is a <italic>t-spanner</italic> of <italic>G</italic> if for all <italic>u, v ε V</italic>,the weighted distance between <italic>u</italic> and <italic>v</italic>… (More)

- Gautam Das, Giri Narasimhan, Jeffrey S. Salowe
- SODA
- 1995

In this paper, we show that any Euclidean graph over a set V of n points in k-dimensional space that satisfies either the leapfrog property or the isolation property has small weight, i.e., has weight O(1) . wt(SMT), where SMT is a Steiner minimal tree of V. Both the leapfrog property as well as the isolation property constrain the way the edges of the… (More)

- Gautam Das, Paul J. Heffernan, Giri Narasimhan
- Symposium on Computational Geometry
- 1993

Let <italic>V</italic> be a set of <italic>n</italic> points in 3-dimensional Euclidean space. A subgraph of the complete Euclidean graph is a <italic>t</italic>-spanner if for any <italic>u</italic> and <italic>v</italic> in <italic>V</italic>, the length of the shortest path from <italic>u</italic> to <italic>v</italic> in the spanner is at most… (More)

- Joachim Gudmundsson, Christos Levcopoulos, Giri Narasimhan
- Nord. J. Comput.
- 2001

- Esther M. Arkin, Joseph S. B. Mitchell, Giri Narasimhan
- Symposium on Computational Geometry
- 1998

WC study a variety of geometric network optimization prob lcms on a set of points, in which we are given a resource bound, a, on the total length of the network, and our ob jcctivc is to maximize the number of points visited (or the total “value” of points visited), In particular, we resolve the well-publicized open problem on the approximabiity of the… (More)