Results 1  10
of
70
Tree Automata, MuCalculus and Determinacy (Extended Abstract)
 IN PROCEEDINGS OF THE 32ND ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, FOCS ’91
, 1991
"... We show that the propositional MuCalculus is equivalent in expressive power to finite automata on infinite trees. Since complementation is trivial in the MuCalculus, our equivalence provides a radically simplified, alternative proof of Rabin's complementation lemma for tree automata, which is the ..."
Abstract

Cited by 215 (4 self)
 Add to MetaCart
We show that the propositional MuCalculus is equivalent in expressive power to finite automata on infinite trees. Since complementation is trivial in the MuCalculus, our equivalence provides a radically simplified, alternative proof of Rabin's complementation lemma for tree automata, which is the heart of one of the deepest decidability results. We also show how MuCalculus can be used to establish determinacy of infinite games used in earlier proofs of complementation lemma, and certain games used in the theory of online algorithms.
An optimal online algorithm for metrical task systems
 Journal of the ACM
, 1992
"... Abstract. In practice, almost all dynamic systems require decisions to be made online, without full knowledge of their future impact on the system. A general model for the processing of sequences of tasks is introduced, and a general online decnion algorithm is developed. It is shown that, for an ..."
Abstract

Cited by 186 (9 self)
 Add to MetaCart
Abstract. In practice, almost all dynamic systems require decisions to be made online, without full knowledge of their future impact on the system. A general model for the processing of sequences of tasks is introduced, and a general online decnion algorithm is developed. It is shown that, for an important algorithms. class of special cases, this algorithm is optimal among all online Specifically, a task system (S. d) for processing sequences of tasks consists of a set S of states and a cost matrix d where d(i, j) is the cost of changing from state i to state j (we assume that d satisfies the triangle inequality and all diagonal entries are f)). The cost of processing a given task depends on the state of the system. A schedule for a sequence T1, T2,..., Tk of tasks is a ‘equence sl,s~,..., Sk of states where s ~ is the state in which T ’ is processed; the cost of a schedule is the sum of all task processing costs and state transition costs incurred. An online scheduling algorithm is one that chooses s, only knowing T1 Tz ~.. T’. Such an algorithm is wcompetitive if, on any input task sequence, its cost is within an additive constant of w times the optimal offline schedule cost. The competitive ratio w(S, d) is the infimum w for which there is a wcompetitive online scheduling algorithm for (S, d). It is shown that w(S, d) = 2 ISI – 1 for eoery task system in which d is symmetric, and w(S, d) = 0(1 S]2) for every task system. Finally, randomized online scheduling algorithms are introduced. It is shown that for the uniform task system (in which d(i, j) = 1 for all i, j), the expected competitive ratio w(S, d) =
Competitive Paging Algorithms
, 1991
"... The paging problem is that of deciding which pages to keep in a memory of k ..."
Abstract

Cited by 164 (22 self)
 Add to MetaCart
The paging problem is that of deciding which pages to keep in a memory of k
Competitive Paging With Locality of Reference
 Journal of Computer and System Sciences
, 1991
"... Abstract The SleatorTarjan competitive analysis of paging [Comm. of the ACM; 28:202 208, 1985] gives us the ability to make strong theoretical statements about the performance of paging algorithms without making probabilistic assumptions on the input. Nevertheless practitioners voice reservations ..."
Abstract

Cited by 121 (3 self)
 Add to MetaCart
Abstract The SleatorTarjan competitive analysis of paging [Comm. of the ACM; 28:202 208, 1985] gives us the ability to make strong theoretical statements about the performance of paging algorithms without making probabilistic assumptions on the input. Nevertheless practitioners voice reservations about the model, citing its inability to discern between LRU and FIFO (algorithms whose performances differ markedly in practice), and the fact that the theoretical competitiveness of LRU is much larger than observed in practice. In addition, we would like to address the following important question: given some knowledge of a program's reference pattern, can we use it to improve paging performance on that program?
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)
 Add to MetaCart
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.
Competitive Algorithms for Distributed Data Management
 In Proceedings of the 24th Annual ACM Symposium on Theory of Computing
"... We deal with the competitive analysis of algorithms for managing data in a distributed environment. We deal with the file allocation problem ([DF], [ML]), where copies of a file may be be stored in the local storage of some subset of processors. Copies may be replicated and discarded over time so ..."
Abstract

Cited by 100 (8 self)
 Add to MetaCart
We deal with the competitive analysis of algorithms for managing data in a distributed environment. We deal with the file allocation problem ([DF], [ML]), where copies of a file may be be stored in the local storage of some subset of processors. Copies may be replicated and discarded over time so as to optimize communication costs, but multiple copies must be kept consistent and at least one copy must be stored somewhere in the network at all times. We deal with competitive algorithms for minimizing communication costs, over arbitrary sequences of reads and writes, and arbitrary network topologies. We define the constrained file allocation problem to be the solution of many individual file allocation problems simultaneously, subject to the constraints of local memory size. We give competitive algorithms for this problem on the uniform network topology. We then introduce distributed competitive algorithms for online data tracking (a generalization of mobile user tracking [AP1...
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. ..."
Abstract

Cited by 76 (2 self)
 Add to MetaCart
We study the design and analysis of randomized online algorithms.
New Results on Server Problems
 SIAM Journal on Discrete Mathematics
, 1990
"... In the kserver problem, we must choose how k mobile servers will serve each of a sequence of requests, making our decisions in an online manner. We exhibit an optimal deterministic online strategy when the requests fall on the real line. For the weightedcache problem, in which the cost of moving t ..."
Abstract

Cited by 73 (7 self)
 Add to MetaCart
In the kserver problem, we must choose how k mobile servers will serve each of a sequence of requests, making our decisions in an online manner. We exhibit an optimal deterministic online strategy when the requests fall on the real line. For the weightedcache problem, in which the cost of moving to x from any other point is w(x), the weight of x, we also provide an optimal deterministic algorithm. We prove the nonexistence of competitive algorithms for the asymmetric twoserver problem, and of memoryless algorithms for the weightedcache problem. We give a fast algorithm for offline computing of an optimal schedule, and show that finding an optimal offline schedule is at least as hard as the assignment problem. 1 Introduction The kserver problem can be stated as follows. We are given a metric space M , and k servers which move among the points of M , each occupying one point of M . Repeatedly, a request (a point x 2 M) appears. To serve x, each server moves some distance, possibly...
Online admission control and circuit routing for high performance computing and communication
, 1994
"... This paper considers the problems of admission control and virtual circuit routing in high performance computing and communication systems. Admission control and virtual circuit routing problems arise in numerous applications, including videoservers, realtime database servers, and the provision of ..."
Abstract

Cited by 69 (7 self)
 Add to MetaCart
This paper considers the problems of admission control and virtual circuit routing in high performance computing and communication systems. Admission control and virtual circuit routing problems arise in numerous applications, including videoservers, realtime database servers, and the provision of permanent virtual channels in largescale communications networks. The paper describes both upper and lower bounds on the competitive ratio of algorithms for admission control and virtual circuit routing in trees, arrays, and hypercubes (the networks most commonly used in conjunction with high performance computing and communication). Our results include optimal algorithms for admission control and virtual circuit routing in trees, as well as the first competitive algorithms for these problems on nontree networks. A key result of our research is the development of online algorithms that substantially outperform the greedybased approaches that are used in practice.
The kserver problem
 Computer Science Review
"... The kserver problem is perhaps the most influential online problem: natural, crisp, with a surprising technical depth that manifests the richness of competitive analysis. The kserver conjecture, which was posed more that two decades ago when the problem was first studied within the competitive ana ..."
Abstract

Cited by 66 (5 self)
 Add to MetaCart
The kserver problem is perhaps the most influential online problem: natural, crisp, with a surprising technical depth that manifests the richness of competitive analysis. The kserver conjecture, which was posed more that two decades ago when the problem was first studied within the competitive analysis framework, is still open and has been a major driving force for the development of the area online algorithms. This article surveys some major results for the kserver. 1