The paging problem is that of deciding which pages to keep in a memory of k

We present a randomized linear-time 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 linear-time algorithm for verifying a minimum spanning tree. Our computational model is a unit-cost random-access machine with the restriction that the only operations allowed on edge weights are binary comparisons.

Chernoff--Hoeffding 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 Chernoff--Hoeffding bounds, e.g., the analysis of randomized algorithms for random sampling and oblivious packet routi...

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 NP-oracle. 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 larger---but polynomially related---size. Also, the algorithms can be adapted to learn the class of DNF formulas with hypothesis class consisting of depth-3 -- 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. depth-2 - formulas).

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...

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 fault-rate of paging algorithms. We first draw on the theory of Markov decision processes to characterize the paging algorithmthat achieves optimal fault-rate on any Markov chain. Next, we address the problemof devising a paging strategy with low fault-rate for a given Markov chain. We show that a number of intuitive approaches fail. Our main result is a polynomial-time procedure that, on any Markov chain, will give a paging algorithm with fault-rate 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.

We show that two cooperating robots can learn ex-actly any strongly-connected directed graph with n in-distinguishable nodes in expected tame polynomial in n. We introduce a new type of homing sequence for two robots which helps the robots recognize certain previously-seen nodes. We then present an algorithm in which the robots learn the graph and the homing se-quence simultaneously by wandering actively through the graph. Unlike most previous learning results us-ang homing sequences, our algorithm does not require a teacher to provide counterexamples. Furthermore, the algorithm can use efficiently any additional infor-mation available that distinguishes nodes. We also present an algorithm in which the robots learn by tak-ing random walks. The rate at which a random walk converges to the stationary distribution is character-ized by the conductance of the graph. Our random-walk algorithm learns in expected time polynomial in n and in the inverse of the conductance and is more eficient than the homing-sequence algorithm for high-conductance graphs. 1

In this paper we give deterministic competitive k-server algorithms for all k and all metric spaces. This settles the k-server conjecture [MMS] up to the competitive ratio. The best previous result for general metric spaces was a 3-server randomized competitive algorithm [BKT] and a non-constructive proof that a deterministic 3-server 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

. Certain types of routing, scheduling, and resource-allocation problems in a distributed setting can be modeled as edge-coloring problems. We present fast and simple randomized algorithms for edge coloring a graph in the synchronous distributed point-to-point 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...

In this paper, we analyze the ability of several bounded-degree networks that are commonly used for parallel computation to tolerate faults. Among other things, we show that an N-node butterfly containing N 1\Gammaffl worst-case faults (for any constant ffl ? 0) can emulate a fault-free 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 worst-case faults without suffering more than a constant-factor slowdown in performance. We also show that an N-node butterfly whose nodes fail with some constant probability p can emulate a fault-free 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...