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110
BEYOND COMPETITIVE ANALYSIS
, 2000
"... The competitive analysis of online algorithms has been criticized as being too crude and unrealistic. We propose refinements of competitive analysis in two directions: The first restricts the power of the adversary by allowingonly certain input distributions, while the other allows for comparisons ..."
Abstract

Cited by 118 (3 self)
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The competitive analysis of online algorithms has been criticized as being too crude and unrealistic. We propose refinements of competitive analysis in two directions: The first restricts the power of the adversary by allowingonly certain input distributions, while the other allows for comparisons between information regimes for online decisionmaking. We illustrate the first with an application to the paging problem; as a byproduct we characterize completely the work functions of this important special case of the kserver problem. We use the second refinement to explore the power of lookahead in server and task systems.
The Power of a Pebble: Exploring and Mapping Directed Graphs
, 1998
"... Exploring and mapping an unknown environment is a fundamental problem, which is studied in various contexts. Many works have focused on finding efficient solutions to restricted versions of the problem. In this paper, we consider a model that makes very limited assumptions on the environment and ..."
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Cited by 104 (4 self)
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Exploring and mapping an unknown environment is a fundamental problem, which is studied in various contexts. Many works have focused on finding efficient solutions to restricted versions of the problem. In this paper, we consider a model that makes very limited assumptions on the environment and solve the mapping problem in this general setting. We model
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 88 (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 ...
Exploring Unknown Environments
 SIAM Journal on Computing
, 1997
"... We consider exploration problems where a robot has to construct a complete map of an unknown environment. We assume that the environment is modeled by a directed, strongly connected graph. The robot's task is to visit all nodes and edges of the graph using the minimum number R of edge traversals ..."
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Cited by 86 (3 self)
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We consider exploration problems where a robot has to construct a complete map of an unknown environment. We assume that the environment is modeled by a directed, strongly connected graph. The robot's task is to visit all nodes and edges of the graph using the minimum number R of edge traversals. Koutsoupias [16] gave a lower bound for R of #(d 2 m), and Deng and Papadimitriou [12] showed an upper bound of d O(d) m, where m is the number edges in the graph and d is the minimum number of edges that have to be added to make the graph Eulerian. We give the first subexponential algorithm for this exploration problem, which achieves an upper bound of d O(logd) m. We also show a matching lower bound of d #(logd) m for our algorithm. Additionally, we give lower bounds of 2 #(d) m, resp. d #(logd) m for various other natural exploration algorithms. 1 Introduction Suppose that a robot has to construct a complete map of an unknown environment using a path that is as sho...
The minimum latency problem
 In Proceedings of the Symposium on Theory of Computing
, 1994
"... We are given a set of points pl,...,p. and a symmetric distance matrix (o!ij) giving the distance between pi and pj. We wish to construct a tour that minimizes ~~=1 1(z), where l(i) is ..."
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Cited by 82 (7 self)
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We are given a set of points pl,...,p. and a symmetric distance matrix (o!ij) giving the distance between pi and pj. We wish to construct a tour that minimizes ~~=1 1(z), where l(i) is
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 76 (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 60 (4 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...
EnergyEfficient Algorithms for . . .
, 2007
"... We study scheduling problems in batteryoperated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadlinebased settings, in this article we are interested in schedules that guarantee good respons ..."
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Cited by 59 (2 self)
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We study scheduling problems in batteryoperated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadlinebased settings, in this article we are interested in schedules that guarantee good response times. More specifically, our goal is to schedule a sequence of jobs on a variablespeed processor so as to minimize the total cost consisting of the energy consumption and the total flow time of all jobs. We first show that when the amount of work, for any job, may take an arbitrary value, then no online algorithm can achieve a constant competitive ratio. Therefore, most of the article is concerned with unitsize jobs. We devise a deterministic constant competitive online algorithm and show that
Competitive kServer Algorithms
 Journal of Computer and System Sciences
, 1990
"... In this paper we give deterministic competitive kserver algorithms for all k and all metric spaces. This settles the kserver conjecture [MMS] up to the competitive ratio. The best previous result for general metric spaces was a 3server randomized competitive algorithm [BKT] and a nonconstructive ..."
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Cited by 55 (4 self)
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In this paper we give deterministic competitive kserver algorithms for all k and all metric spaces. This settles the kserver conjecture [MMS] up to the competitive ratio. The best previous result for general metric spaces was a 3server randomized competitive algorithm [BKT] and a nonconstructive proof that a deterministic 3server competitive algorithm exists [BBKTW]. The competitive ratio we can prove is exponential in the number of servers. Thus, the question of the minimal competitive ratio for arbitrary metric spaces is still open. 1