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- Prosenjit Bose, Pat Morin, Ivan Stojmenovic, Jorge Urrutia
- Wireless Networks
- 1999

We consider routing problems in ad hoc wireless networks modeled as unit graphs in which nodes are points in the plane and two nodes can communicate if the distance between them is less than some fixed unit. We describe the first distributed algorithms for routing that do not require duplication of packets or memory at the nodes and yet guarantee that a… (More)

- Prosenjit Bose, Pat Morin
- SIAM J. Comput.
- 1999

We consider online routing algorithms for routing between the vertices of embedded planar straight line graphs. Our results include (1) two deterministic memoryless routing algorithms, one that works for all Delaunay triangulations and the other that works for all regular triangula-tions, (2) a randomized memoryless algorithm that works for all… (More)

- Vida Dujmovic, Pat Morin, David R. Wood
- SIAM J. Comput.
- 2005

A queue layout of a graph consists of a total order of the vertices, and a partition of the edges into queues, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph is its queue-number. A three-dimensional (straight-line grid) drawing of a graph represents the vertices by points in Z 3 and the edges… (More)

- Prosenjit Bose, Pat Morin
- ISAAC
- 2000

- Prosenjit Bose, Andrej Brodnik, +5 authors J. Ian Munro
- Int. J. Comput. Geometry Appl.
- 2000

We consider online routing algorithms for finding paths between the vertices of plane graphs. We show (1) there exists a routing algorithm for arbitrary triangulations that has no memory and uses no randomization, (2) no equivalent result is possible for convex subdivisions, (3) there is no competitive online routing algorithm under the Euclidean distance… (More)

- Prosenjit Bose, Hua Guo, +5 authors Yihui Tang
- Inf. Process. Lett.
- 2008

Bloom filters are a randomized data structure for membership queries dating back to 1970. Bloom filters sometimes give erroneous answers to queries, called false positives. Bloom analyzed the probability of such erroneous answers, called the false-positive rate, and Bloom's analysis has appeared in many publications throughout the years. We show that… (More)

- Stefan Langerman, Pat Morin
- Discrete & Computational Geometry
- 2002

An abstract NP-hard covering problem is presented and xed-parameter tractable algorithms for this problem are described. The running times of the algorithms are expressed in terms of three parameters: n, the number of elements to be covered, k, the number of sets allowed in the covering, and d, the combinatorial dimension of the problem. The rst algorithm… (More)

- Michel Barbeau, Evangelos Kranakis, Danny Krizanc, Pat Morin
- ADHOC-NOW
- 2004

Supporting nodes without Global Positioning System (GPS) capability, in wireless ad hoc and sensor networks, has numerous applications in guidance and surveying systems in use today. At issue is that a procedure be available so that the subset of nodes with GPS capability succeed in supporting the maximum possible number of nodes without GPS capability and… (More)

- Pankaj K. Agarwal, Rolf Klein, +4 authors Michael A. Soss
- Discrete & Computational Geometry
- 2008

The detour and spanning ratio of a graph embedded in measure how well approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe " ! $ # & % ') (time algorithms for computing the detour and spanning ratio of a planar polygonal path. By generalizing these algorithms, we obtain " ! $ # & % 1 0 2) (time algorithms… (More)

- Prosenjit Bose, Vida Dujmovic, Ferran Hurtado, Stefan Langerman, Pat Morin, David R. Wood
- Discrete & Computational Geometry
- 2008

To untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. Pach and Tardos [Discrete Comput. Geom., 2002] asked if every n-vertex geometric planar graph can be untangled while keeping at least n ǫ vertices fixed. We answer this question in the affirmative with ǫ = 1/4. The previous best known… (More)