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13
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 465 (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*: Finding the shortest path with A* in unknown physical environments
 Journal of Artificial Intelligence Research (JAIR
, 2004
"... 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 territory. We introduce the PhysicalA * algorithm (PHA*) for solving this problem. PHA * expands all the man ..."
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Cited by 15 (8 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 territory. We introduce the PhysicalA * algorithm (PHA*) for solving this problem. PHA * expands all the mandatory nodes that A * would expand and returns the shortest path between the two points. However, due to the physical nature of the problem, the complexity of the algorithm is measured by the traveling effort of the moving agent and not by the number of generated nodes, as in standard A*. PHA * is presented as a twolevel algorithm, such that its high level, A*, chooses the next node to be expanded and its low level directs the agent to that node in order to explore it. We present a number of variations for both the highlevel and lowlevel procedures and evaluate their performance theoretically and experimentally. We show that the travel cost of our best variation is fairly close to the optimal travel cost, assuming that the mandatory nodes of A * are known in advance. We then generalize our algorithm to the multiagent case, where a number of cooperative agents are designed to solve the problem. Specifically, we provide an experimental implementation for such a system. It should be noted that the problem addressed here is not a navigation problem, but rather a problem of finding the shortest path between two points for future usage. 1.
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 8 (8 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 ARTIFICIAL INTELLIGENCE
, 1999
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Online Routing in Convex Subdivisions ∗ Prosenjit Bose
"... 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 competit ..."
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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 metric in arbitrary triangulations, and (4) there is no competitive online routing algorithm under the link distance metric even when the input graph is restricted to be a Delaunay, greedy, or minimumweight triangulation. 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 ..."
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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.
Multiagent Physical A * with Large Pheromones
"... Abstract. Physical A * (PHA*) and its multiagent version MAPHA * are algorithms that find the shortest path between two points in an unknown real physical environment with one or many mobile agents [15, 16]. Previous work assumed a complete sharing of knowledge between agents. Here we apply this al ..."
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Abstract. Physical A * (PHA*) and its multiagent version MAPHA * are algorithms that find the shortest path between two points in an unknown real physical environment with one or many mobile agents [15, 16]. Previous work assumed a complete sharing of knowledge between agents. Here we apply this algorithm to a more restricted model of communication which we call large pheromones, where agents communicate by writing and reading data at nodes of the graph that constitutes their environment. Previous works on pheromones usually assumed that only a limited amount of data can be written at each node. The large pheromones model assumes no limitation on the size of the pheromones and thus each agent can write its entire knowledge at a node. We show that with this model of communication the behavior of a multiagent system is almost as good as with complete knowledge sharing. Under this model we also introduce a new type of agent, a communication agent, that is responsible for spreading the knowledge among other agents by moving around the graph and copying pheromones. Experimental results show that the contribution of communication agents is rather limited as data is already spread to other agents very well with large pheromones. keywords: Mobile agents; A*; Shortest path; Pheromones; Multiagent communication models
DOI: 10.1007/s104580053943y
, 2005
"... Abstract. Physical A * (PHA*) and its multiagent version MAPHA * are algorithms that find the shortest path between two points in an unknown real physical environment with one or many mobile ..."
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Abstract. Physical A * (PHA*) and its multiagent version MAPHA * are algorithms that find the shortest path between two points in an unknown real physical environment with one or many mobile