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28
Competitive Paging Algorithms
, 1991
"... The paging problem is that of deciding which pages to keep in a memory of k ..."
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Cited by 164 (22 self)
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The paging problem is that of deciding which pages to keep in a memory of k
A Randomized LinearTime Algorithm to Find Minimum Spanning Trees
, 1994
"... We present a randomized lineartime algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered lineartime algorithm for verifying a minimum spanning tree. Our computational model is a unitcost ra ..."
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Cited by 115 (7 self)
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We present a randomized lineartime algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered lineartime algorithm for verifying a minimum spanning tree. Our computational model is a unitcost randomaccess machine with the restriction that the only operations allowed on edge weights are binary comparisons.
ChernoffHoeffding Bounds for Applications with Limited Independence
 SIAM J. Discrete Math
, 1993
"... ChernoffHoeffding bounds are fundamental tools used in bounding the tail probabilities of the sums of bounded and independent random variables. We present a simple technique which gives slightly better bounds than these, and which more importantly requires only limited independence among the rando ..."
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Cited by 102 (10 self)
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ChernoffHoeffding bounds are fundamental tools used in bounding the tail probabilities of the sums of bounded and independent random variables. We present a simple technique which gives slightly better bounds than these, and which more importantly requires only limited independence among the random variables, thereby importing a variety of standard results to the case of limited independence for free. Additional methods are also presented, and the aggregate results are sharp and provide a better understanding of the proof techniques behind these bounds. They also yield improved bounds for various tail probability distributions and enable improved approximation algorithms for jobshop scheduling. The "limited independence" result implies that a reduced amount of randomness and weaker sources of randomness are sufficient for randomized algorithms whose analyses use the ChernoffHoeffding bounds, e.g., the analysis of randomized algorithms for random sampling and oblivious packet routi...
Oracles and Queries that are Sufficient for Exact Learning
 Journal of Computer and System Sciences
, 1996
"... We show that the class of all circuits is exactly learnable in randomized expected polynomial time using weak subset and weak superset queries. This is a consequence of the following result which we consider to be of independent interest: circuits are exactly learnable in randomized expected poly ..."
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Cited by 82 (5 self)
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We show that the class of all circuits is exactly learnable in randomized expected polynomial time using weak subset and weak superset queries. This is a consequence of the following result which we consider to be of independent interest: circuits are exactly learnable in randomized expected polynomial time with equivalence queries and the aid of an NPoracle. We also show that circuits are exactly learnable in deterministic polynomial time with equivalence queries and a \Sigma 3 oracle. The hypothesis class for the above learning algorithms is the class of circuits of largerbut polynomially relatedsize. Also, the algorithms can be adapted to learn the class of DNF formulas with hypothesis class consisting of depth3  formulas (by the work of Angluin [A90], this is optimal in the sense that the hypothesis class cannot be reduced to DNF formulas, i.e. depth2  formulas).
The power of team exploration: Two robots can learn unlabeled directed graphs
 In Proceedings of the Thirty Fifth Annual Symposium on Foundations of Computer Science
, 1994
"... We show that two cooperating robots can learn exactly any stronglyconnected directed graph with n indistinguishable nodes in expected tame polynomial in n. We introduce a new type of homing sequence for two robots which helps the robots recognize certain previouslyseen nodes. We then present an ..."
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Cited by 66 (5 self)
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We show that two cooperating robots can learn exactly any stronglyconnected directed graph with n indistinguishable nodes in expected tame polynomial in n. We introduce a new type of homing sequence for two robots which helps the robots recognize certain previouslyseen nodes. We then present an algorithm in which the robots learn the graph and the homing sequence simultaneously by wandering actively through the graph. Unlike most previous learning results usang homing sequences, our algorithm does not require a teacher to provide counterexamples. Furthermore, the algorithm can use efficiently any additional information available that distinguishes nodes. We also present an algorithm in which the robots learn by taking random walks. The rate at which a random walk converges to the stationary distribution is characterized by the conductance of the graph. Our randomwalk algorithm learns in expected time polynomial in n and in the inverse of the conductance and is more eficient than the homingsequence algorithm for highconductance graphs. 1
MARKOV PAGING
, 2000
"... This paper considers the problemof paging under the assumption that the sequence of pages accessed is generated by a Markov chain. We use this model to study the faultrate of paging algorithms. We first draw on the theory of Markov decision processes to characterize the paging algorithmthat achieve ..."
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Cited by 60 (4 self)
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This paper considers the problemof paging under the assumption that the sequence of pages accessed is generated by a Markov chain. We use this model to study the faultrate of paging algorithms. We first draw on the theory of Markov decision processes to characterize the paging algorithmthat achieves optimal faultrate on any Markov chain. Next, we address the problemof devising a paging strategy with low faultrate for a given Markov chain. We show that a number of intuitive approaches fail. Our main result is a polynomialtime procedure that, on any Markov chain, will give a paging algorithm with faultrate at most a constant times optimal. Our techniques show also that some algorithms that do poorly in practice fail in the Markov setting, despite known (good) performance guarantees when the requests are generated independently from a probability distribution.
Backwards Analysis of Randomized Geometric Algorithms
 Trends in Discrete and Computational Geometry, volume 10 of Algorithms and Combinatorics
, 1992
"... The theme of this paper is a rather simple method that has proved very potent in the analysis of the expected performance of various randomized algorithms and data structures in computational geometry. The method can be described as "analyze a randomized algorithm as if it were running backwards in ..."
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Cited by 60 (0 self)
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The theme of this paper is a rather simple method that has proved very potent in the analysis of the expected performance of various randomized algorithms and data structures in computational geometry. The method can be described as "analyze a randomized algorithm as if it were running backwards in time, from output to input." We apply this type of analysis to a variety of algorithms, old and new, and obtain solutions with optimal or near optimal expected performance for a plethora of problems in computational geometry, such as computing Delaunay triangulations of convex polygons, computing convex hulls of point sets in the plane or in higher dimensions, sorting, intersecting line segments, linear programming with a fixed number of variables, and others. 1 Introduction The curious phenomenon that randomness can be used profitably in the solution of computational tasks has attracted a lot of attention from researchers in recent years. The approach has proved useful in such diverse area...
Randomized Distributed Edge Coloring via an Extension of the ChernoffHoeffding Bounds
 SIAM J. Comput
, 1997
"... . Certain types of routing, scheduling, and resourceallocation problems in a distributed setting can be modeled as edgecoloring problems. We present fast and simple randomized algorithms for edge coloring a graph in the synchronous distributed pointtopoint model of computation. Our algorithms co ..."
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Cited by 56 (9 self)
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. Certain types of routing, scheduling, and resourceallocation problems in a distributed setting can be modeled as edgecoloring problems. We present fast and simple randomized algorithms for edge coloring a graph in the synchronous distributed pointtopoint model of computation. Our algorithms compute an edge coloring of a graph G with n nodes and maximum degree # with at most 1.6# +O(log 1+# n) colors with high probability (arbitrarily close to 1) for any fixed #>0; they run in polylogarithmic time. The upper bound on the number of colors improves upon the (2#  1)coloring achievable by a simple reduction to vertex coloring. To analyze the performance of our algorithms, we introduce new techniques for proving upper bounds on the tail probabilities of certain random variables. The Cherno#Hoe#ding bounds are fundamental tools that are used very frequently in estimating tail probabilities. However, they assume stochastic independence among certain random variables, which may n...
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
On the Fault Tolerance of Some Popular BoundedDegree Networks
 SIAM Journal on Computing
, 1992
"... In this paper, we analyze the ability of several boundeddegree networks that are commonly used for parallel computation to tolerate faults. Among other things, we show that an Nnode butterfly containing N 1\Gammaffl worstcase faults (for any constant ffl ? 0) can emulate a faultfree butterfly ..."
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Cited by 44 (7 self)
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In this paper, we analyze the ability of several boundeddegree networks that are commonly used for parallel computation to tolerate faults. Among other things, we show that an Nnode butterfly containing N 1\Gammaffl worstcase faults (for any constant ffl ? 0) can emulate a faultfree butterfly of the same size with only constant slowdown. Similar results are proved for the shuffleexchange graph. Hence, these networks become the first connected boundeddegree networks known to be able to sustain more than a constant number of worstcase faults without suffering more than a constantfactor slowdown in performance. We also show that an Nnode butterfly whose nodes fail with some constant probability p can emulate a faultfree version of itself with a slowdown of 2 O(log N) , which is a very slowly increasing function of N . The proofs of these results combine the technique of redundant computation with new algorithms for (packet) routing around faults in hypercubic networks. Tech...