In this paper we study the problem of on-line allocation of routes to virtual circuits (both point-to-point and multicast) where the goal is to route all requests while minimizing the required bandwidth. We concentrat...
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In this paper we study the problem of on-line allocation of routes to virtual circuits (both point-to-point and multicast) where the goal is to route all requests while minimizing the required bandwidth. We concentrate on the case of permanent virtual circuits (i.e., once a circuit is established, it exists forever), and describe an algorithm that achieves an O(log n) competitive ratio with respect to maximum congestion, where n is the number of nodes in the network. Informally, our results show that instead of knowing all of the future requests, it is sufficient to increase the bandwidth of the communication links by an O(log n) factor. We also show that this result is tight, that is, for any on-line algorithm there exists a scenario in which Omega(log n) increase in bandwidth is necessary in directed networks. We view virtual circuit routing as a generalization of an on-line load balancing problem, defined as follows: jobs arrive on line and each job must be assigned to one of the machines immediately upon arrival. Assigning a job to a machine increases the machine's load by an amount that depends both on the job and on the machine. The goal is to minimize the maximum load. For the related machines case, we describe the first algorithm that achieves constant competitive ratio. For the unrelated case (with n machines), we describe a new method that yields O(log n)-competitive algorithm. This stands in contrast to the natural greedy approach, whose competitive ratios is exactly n.
We extend the definition of Metrical Task System, introduced by Borodin et al. in [4]. In the extended definition, a system is described by the underlying metric space of states M as well as a set of allowable tasks T...
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We extend the definition of Metrical Task System, introduced by Borodin et al. in [4]. In the extended definition, a system is described by the underlying metric space of states M as well as a set of allowable tasks T. Any request to an algorithm must be a member of T. The extension makes the model powerful enough to characterize completely many important on-line problems. We consider methods of designing competitive algorithms given the description of a system (M, I). In particular, we show that it is PSPACE-hard to determine the behavior of a c(M, I)-competitive algorithm, where c(M, I) is the best possible competitive ratio on (M, I). In addition, we show a simple, polynomial-rime algorithm for task systems [U-n, I] (where U-n is the uniform metric space on n nodes) that achieves a competitive ratio of O(log n . C(M, T)).
We significantly improve the previous lower bounds on the performance of randomized algorithms for on-line scheduling jobs on m identical machines. We also show that a natural idea for constructing an algorithm with m...
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We significantly improve the previous lower bounds on the performance of randomized algorithms for on-line scheduling jobs on m identical machines. We also show that a natural idea for constructing an algorithm with matching performance does not work. (C) 1997 Elsevier Science B.V.
COUNTER algorithms, a family of randomized algorithms for the list update problem, were introduced by Reingold, Westbrook, and Sleator (1994). They showed that for any epsilon > 0, there exist COUNTER algorithms th...
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COUNTER algorithms, a family of randomized algorithms for the list update problem, were introduced by Reingold, Westbrook, and Sleator (1994). They showed that for any epsilon > 0, there exist COUNTER algorithms that achieve a competitive ratio of root 3 + epsilon. In this paper we use a mixture of two COUNTER algorithms to achieve a competitiveness of 12/7, which is less than root 3. Furthermore, we demonstrate that it is impossible to prove a competitive ratio smaller than 12/7 for any mixture of COUNTER algorithms using the type of potential function argument that has been used so far. We also provide new lower bounds for the competitiveness of COUNTER algorithms in the standard cost model, including a 1.625 lower bound for the variant BIT and a matching 12/7 lower bound for our algorithm. (C) 1997 Elsevier Science B.V.
We introduce a new model of lookahead for on-line paging algorithms and study several algorithms using this model. A paging algorithm is on-line with strong lookahead l if it sees the present request and a sequence of...
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We introduce a new model of lookahead for on-line paging algorithms and study several algorithms using this model. A paging algorithm is on-line with strong lookahead l if it sees the present request and a sequence of future requests that contains l pairwise distinct pages. We show that strong lookahead has practical as well as theoretical importance and improves the competitive factors of on-line paging algorithms. This is the first model of lookahead having such properties. In addition to lower bounds we present a number of deterministic and randomized on-line paging algorithms with strong lookahead which are optimal or nearly optimal.
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 do...
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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 (obstacle-free) 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 maze traversal. We also show scenes where randomized algorithms are provably better than deterministic algorithms.
The function LM, which arises in the pinwheel scheduling problem, was previously known to be computable in polynomial time. In this paper we present a practical algorithm to compute LM that runs in linear time.
The function LM, which arises in the pinwheel scheduling problem, was previously known to be computable in polynomial time. In this paper we present a practical algorithm to compute LM that runs in linear time.
This paper gives the average distance analysis for the Euclidean tree constructed by a simple greedy but efficient algorithm of the on-line Steiner tree problem. The algorithm accepts the data one by one following the...
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This paper gives the average distance analysis for the Euclidean tree constructed by a simple greedy but efficient algorithm of the on-line Steiner tree problem. The algorithm accepts the data one by one following the order of input sequence. When a point arrives, the algorithm adds the shortest edge, between the new point and the points arriving already, to the previously constructed tree to form a new tree. We first show that, given n points uniformly on a unit disk in the plane, the expected Euclidean distance between a point and its j(th) (1 less than or equal to j less than or equal to n - 1) nearest neighbor is less than or equal to (5/3)root/j/n when n is large. Based upon this result, we show that the expected length of the tree constructed by the on-line algorithm is not greater than 4.34 times the expected length of the minimum Steiner tree when the number of input points is large.
It is shown that the work function algorithm for the 2-evader problem has competitive ratio m - 2 for all metric spaces with m points, This settles the k-server conjecture for metric spaces with k + 2 points.
It is shown that the work function algorithm for the 2-evader problem has competitive ratio m - 2 for all metric spaces with m points, This settles the k-server conjecture for metric spaces with k + 2 points.
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