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The Quickhull algorithm for convex hulls
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1996
"... The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algo ..."
Abstract

Cited by 456 (0 self)
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The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floatingpoint arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick ” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.
PHA*: Performing A* in Unknown Physical Environments
 In AAMAS 2002
, 2002
"... We address the problem of finding the shortest path between two points in an unknown real physical environment, where a traveling agent must move around in the environment to explore unknown territories. We present the PhysicalA* algorithm (PHA*) to solve such a problem. PHA* is a twolevel algorith ..."
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Cited by 7 (7 self)
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We address the problem of finding the shortest path between two points in an unknown real physical environment, where a traveling agent must move around in the environment to explore unknown territories. We present the PhysicalA* algorithm (PHA*) to solve such a problem. PHA* is a twolevel algorithm in which the upper level is A*, which chooses the next node to expand and the lower level directs the agent to that node in order to explore it. The complexity of this algorithm is measured by the traveling effort of the moving agent and not by the number of generated nodes as in classical A*. We present a number of variations of both the upper level and lower level algorithms and compare them both experimentally and theoretically. We then generalize our algorithm to the multiagent case where a number of cooperative agents are designed to solve this problem and show experimental implementation for such a system.
Utilitybased OnLine Exploration for Repeated Navigation in an Embedded Graph
 Artificial Intelligence
, 1998
"... In this paper, we address the tradeoff between exploration and exploitation for agents which need to learn more about the structure of their environment in order to perform more effectively. For example, a robot may need to learn the most efficient routes between important sites in its environment. ..."
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Cited by 4 (3 self)
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In this paper, we address the tradeoff between exploration and exploitation for agents which need to learn more about the structure of their environment in order to perform more effectively. For example, a robot may need to learn the most efficient routes between important sites in its environment. We compare online and offline exploration for a repeated task, where the agent is given some particular task to perform some number of times. Tasks are modeled as navigation on a graph embedded in the plane. This paper describes a utilitybased online exploration algorithm for repeated tasks, which takes into account both the costs and potential benefits (over future task repetitions) of different exploratory actions. Exploration is performed in a greedy fashion, with the locally optimal exploratory action performed on each task repetition. We experimentally evaluated our utilitybased online algorithm against a heuristic search algorithm for offline exploration as well as a randomized ...
UtilityBased MultiAgent System for Performing Repeated Navigation Tasks ∗
"... Suppose that a number of mobile agents need to travel back and forth between two locations in an unknown environment a given number of times. These agents need to find the right balance between exploration of the environment and performing the actual task via a known suboptimal path. Each agent shou ..."
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Cited by 2 (1 self)
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Suppose that a number of mobile agents need to travel back and forth between two locations in an unknown environment a given number of times. These agents need to find the right balance between exploration of the environment and performing the actual task via a known suboptimal path. Each agent should decide whether to follow the best known path or to devote its effort for further exploration of the graph so as to improve the path for future usage. We introduce a utilitybased approach which chooses its next job such that the estimation of global utility is maximized. We compare this approach to a stochastic greedy approach which chooses its next job randomaly so as to increase the diversity of the known graph. We apply these approaches to different environments and to different communication paradigms. Experimental results show that an intelligent utilitybased multiagent system outperforms a stochastic greedy multiagent system. In addition the utilitybased approach was robust under inaccurate input and limitation of the communication abilities.
Interleaved vs. a priori exploration for repeated navigation in a partiallyknown graph
 International Journal of Pattern Recognition and Arti cial Intelligence
, 1999
"... 1 ..."
Be’erSheva
"... Suppose that a number of mobile agents need to travel back and forth between two locations in an unknown environment a given number of times. These agents need to find the right balance between exploration of the environment and performing the actual task via a known suboptimal path. Each agent shou ..."
Abstract
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Suppose that a number of mobile agents need to travel back and forth between two locations in an unknown environment a given number of times. These agents need to find the right balance between exploration of the environment and performing the actual task via a known suboptimal path. Each agent should decide whether to follow the best known path or to devote its effort for further exploration of the graph so as to improve the path for future usage. We introduce a utilitybased approach which chooses its next job such that the estimation of global utility is maximized. We compare this approach to a stochastic greedy approach which chooses its next job randomaly so as to increase the diversity of the known graph. We apply these approaches to different environments and to different communication paradigms. Experimental results show that an intelligent utilitybased multiagent system outperforms a stochastic greedy multiagent system. In addition the utilitybased approach was robust under inaccurate input and limitation of the communication abilities.