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146
Routing with Guaranteed Delivery in ad hoc Wireless Networks
, 2001
"... 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 ..."
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Cited by 856 (87 self)
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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 packet is delivered to its destination. These algorithms can be extended to yield algorithms for broadcasting and geocasting that do not require packet duplication. A byproduct of our results is a simple distributed protocol for extracting a planar subgraph of a unit graph. We also present simulation results on the performance of our algorithms.
Geometric Shortest Paths and Network Optimization
 Handbook of Computational Geometry
, 1998
"... Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to ..."
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Cited by 194 (15 self)
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Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to be the sum of the weights of the edges that comprise it. Efficient algorithms are well known for this problem, as briefly summarized below. The shortest path problem takes on a new dimension when considered in a geometric domain. In contrast to graphs, where the encoding of edges is explicit, a geometric instance of a shortest path problem is usually specified by giving geometric objects that implicitly encode the graph and its edge weights. Our goal in devising efficient geometric algorithms is generally to avoid explicit construction of the entire underlying graph, since the full induced graph may be very large (even exponential in the input size, or infinite). Computing an optimal
Online Routing in Triangulations
 IN PROC. OF THE 10 TH ANNUAL INT. SYMP. ON ALGORITHMS AND COMPUTATION ISAAC
, 1999
"... 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 ..."
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Cited by 138 (14 self)
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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.
The Power of a Pebble: Exploring and Mapping Directed Graphs
 A PRELIMINARY VERSION OF THIS WORK APPEARED IN STOC `98
, 1998
"... ..."
Navigating In Unfamiliar Geometric Terrain
, 1991
"... . Consider a robot that has to travel from a start location s to a target t in an environment with opaque obstacles that lie in its way. The robot always knows its current absolute position and that of the target. It does not, however, know the positions and extents of the obstacles in advance; rath ..."
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Cited by 95 (3 self)
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. Consider a robot that has to travel from a start location s to a target t in an environment with opaque obstacles that lie in its way. The robot always knows its current absolute position and that of the target. It does not, however, know the positions and extents of the obstacles in advance; rather, it finds out about obstacles as it encounters them. We compare the distance walked by the robot in going from s to t to the length of the shortest (obstaclefree) path between s and t in the scene. We describe and analyze robot strategies that minimize this ratio for different kinds of scenes. In particular, we consider the cases of rectangular obstacles aligned with the axes, rectangular obstacles in more general orientations, and wider classes of convex bodies both in two and three dimensions. For many of these situations, our algorithms are optimal up to constant factors. We study scenes with nonconvex obstacles, which are related to the study of mazetraversal. We also show scenes ...
An Improved Approximation Ratio for the Minimum Latency Problem
 Mathematical Programming
, 1996
"... Given a tour visiting n points in a metric space, the latency of one of these points p is the distance traveled in the tour before reaching p. The minimum latency problem asks for a tour passing through n given points for which the total latency of the n points is minimum; in effect, we are seekin ..."
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Cited by 87 (2 self)
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Given a tour visiting n points in a metric space, the latency of one of these points p is the distance traveled in the tour before reaching p. The minimum latency problem asks for a tour passing through n given points for which the total latency of the n points is minimum; in effect, we are seeking the tour with minimum average "arrival time." This problem has been studied in the operations research literature, where it has also been termed the "deliveryman problem" and the "traveling repairman problem." The approximability of the minimum latency problem was first considered by Sahni and Gonzalez in 1976; however, unlike the classical traveling salesman problem, it is not easy to give any constantfactor approximation algorithm for the minimum latency problem. Recently, Blum, Chalasani, Coppersmith, Pulleyblank, Raghavan, and Sudan gave the first such algorithm, obtaining an approximation ratio of 144. In this work, we present an algorithm which improves this ratio to 21:55. The dev...
Robot Navigation in Unknown Terrains: Introductory Survey of NonHeuristic Algorithms
, 1993
"... vii 1 ..."
Random Walks on Weighted Graphs, and Applications to Online Algorithms (Extended
 Journal of the ACM
, 1990
"... We study the design and analysis of randomized online algorithms. ..."
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Cited by 78 (2 self)
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We study the design and analysis of randomized online algorithms.
Searching in an Unknown Environment: An Optimal Randomized Algorithm for the CowPath Problem
, 1993
"... Searching for a goal is a central and extensively studied problem in computer science. In classical searching problems, the cost of a search function is simply the number of queries made to an oracle that knows the position of the goal. In many robotics problems, as well as in problems from other ar ..."
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Cited by 69 (3 self)
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Searching for a goal is a central and extensively studied problem in computer science. In classical searching problems, the cost of a search function is simply the number of queries made to an oracle that knows the position of the goal. In many robotics problems, as well as in problems from other areas, we want to charge a cost proportional to the distance between queries (e.g., the time required to travel between two query points). With this cost function in mind, the abstract problem known as the wlane cowpath problem was designed. There are known optimal deterministic algorithms for the cowpath problem, and we give the first randomized algorithm in this paper. We show that our algorithm is optimal for two paths (w = 2), and give evidence that it is optimal for larger values of w. Subsequent to the preliminary of version of this paper, Kao, Ma, Sipser, and Yin [10] have shown that our algorithm is indeed optimal for all w 2. Our randomized algorithm gives expected performance tha...
Online Scheduling
, 2003
"... In this chapter, we summarize research efforts on several different problems that fall under the rubric of online scheduling. In online scheduling, the scheduler receives jobs that arrive over time, and generally must schedule the jobs without any knowledge of the future. The lack of knowledge of th ..."
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Cited by 64 (5 self)
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In this chapter, we summarize research efforts on several different problems that fall under the rubric of online scheduling. In online scheduling, the scheduler receives jobs that arrive over time, and generally must schedule the jobs without any knowledge of the future. The lack of knowledge of the future generally precludes the scheduler from guaranteeing optimal schedules. Thus much research has been focused on finding scheduling algorithms that guarantee schedules that are in some way not too far from optimal. We focus on problems that arise within the ubiquitous clientserver setting. In a clientserver system, there are many clients and one server (or a perhaps a few servers). Clients submit requests for service to the server(s) over time. In the language of scheduling, a server is a processor, and a request is a job. Applications that motivate the research we survey include multiuser operating systems such as Unix and Windows, web servers, database servers, name servers, and load...