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 Resource Type:
 Article
 Creator:
 Morin, Pat, Hurtado, Ferran, Bose, Prosenjit, and Carmi, Paz
 Abstract:
 We prove that, for every simple polygon P having k ≥ 1 reflex vertices, there exists a point q ε P such that every halfpolygon that contains q contains nearly 1/2(k + 1) times the area of P. We also give a family of examples showing that this result is the best possible.
 Date Created:
 20110401

 Resource Type:
 Conference Proceeding
 Creator:
 Morin, Pat and Bose, Prosenjit
 Abstract:
 We consider online routing strategies for routing between the vertices of embedded planar straight line graphs. Our results include (1) two deterministic memoryless routing strategies, one that works for all Delaunay triangulations and the other that works for all regular triangulations, (2) a randomized memoryless strategy that works for all triangulations, (3) an O(1) memory strategy that works for all convex subdivisions, (4) an O(1) memory strategy that approximates the shortest path in Delaunay triangulations, and (5) theoretical and experimental results on the competitiveness of these strategies.
 Date Created:
 19990101

 Resource Type:
 Conference Proceeding
 Creator:
 Kranakis, Evangelos, Morin, Pat, and Krizanc, Danny
 Abstract:
 We present a tradeoff between the expected time for two identical agents to rendezvous on a synchronous, anonymous, oriented ring and the memory requirements of the agents. In particular, we show that there exists a 2t state agent, which can achieve rendezvous on an n node ring in expected time O( n 2/2 t ∈+∈2 t ) and that any t/2 state agent requires expected time Ω( n 2/2 t ). As a corollary we observe that Θ(loglogn) bits of memory are necessary and sufficient to achieve rendezvous in linear time.
 Date Created:
 20080512

 Resource Type:
 Conference Proceeding
 Creator:
 Bose, Prosenjit, Howat, John, and Morin, Pat
 Abstract:
 The time required for a sequence of operations on a data structure is usually measured in terms of the worst possible such sequence. This, however, is often an overestimate of the actual time required. Distributionsensitive data structures attempt to take advantage of underlying patterns in a sequence of operations in order to reduce time complexity, since access patterns are nonrandom in many applications. Unfortunately, many of the distribution sensitive structures in the literature require a great deal of space overhead in the form of pointers. We present a dictionary data structure that makes use of both randomization and existing spaceefficient data structures to yield very low space overhead while maintaining distribution sensitivity in the expected sense.
 Date Created:
 20090914

 Resource Type:
 Conference Proceeding
 Creator:
 Bose, Prosenjit, Maheshwari, Anil, He, Meng, and Morin, Pat
 Abstract:
 We present a succinct representation of a set of n points on an n×n grid using bits to support orthogonal range counting in time, and range reporting in time, where k is the size of the output. This achieves an improvement on query time by a factor of upon the previous result of Mäkinen and Navarro [1], while using essentially the informationtheoretic minimum space. Our data structure not only can be used as a key component in solutions to the general orthogonal range search problem to save storage cost, but also has applications in text indexing. In particular, we apply it to improve two previous spaceefficient text indexes that support substring search [2] and positionrestricted substring search [1]. We also use it to extend previous results on succinct representations of sequences of small integers, and to design succinct data structures supporting certain types of orthogonal range query in the plane.
 Date Created:
 20090914