STOC

We study the problem of clustering points in a metric space so as to minimize the sum of cluster diameters. Significantly improving on previous results, we present a primal-dual based constant factor approximation algorithm for this problem. We present ...

The min-sum k-clustering problem in a metric space is to find a partition of the space into k clusters as to minimize the total sum of distances between pairs of points assigned to the same cluster. We give the first polynomial time non-trivial ...

In this paper, we analyze local search heuristics for the k-median and facility location problems. We define the {\em locality gap\/} of a local search procedure as the maximum ratio of a locally optimum solution (obtained using this procedure) to the ...

We consider opening facilities in order to gain a profit. We are given a set of demand points, and we must open some set of facilities such that every demand may be satisfied from a local facility and the total profit gained in this process is ...

We define and analyze quantum computational variants of random walks on one-dimensional lattices. In particular, we analyze a quantum analog of the symmetric random walk, which we call the Hadamard walk. Several striking differences between the quantum ...

We set the ground for a theory of quantum walks on graphs-the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible. However, by ...

In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing normality of a ...

We provide positive and negative results concerning the “standard method” of identifying a hidden subgroup of a nonabelian group using a quantum computer.

The parametric minimax problem, which finds the parameter value minimizing the weight of a solution of a combinatorial maximization problem, is a fundamental problem in sensitivity analysis. Moreover, several problems in computational geometry can be ...

We study the problem of minimizing weighted flow time on a single machine in the preemptive setting. We present an O(\log^2 P)-competitive semi-online algorithm where P is the ratio of the maximum and minimum processing times of jobs in the system. In ...

Scheduling a sequence of jobs released over time when the processing time of a job is only known at its completion is a classical problem in CPU scheduling in time sharing operating systems. A widely used measure for the responsiveness of the system is ...

We study the problem of optimizing the performance of a system shared by selfish, noncooperative users. We consider the concrete setting of scheduling jobs on a set of shared machines with load-dependent latency functions specifying the length of time ...

A model of quantum computation based on unitary matrix operations was introduced by Feynman and Deutsch. It has been asked whether the power of this model exceeds that of classical Turing machines. We show here that a significant class of these quantum ...

One of the most intriguing facts about communication using quantum states is that these states cannot be used to transmit more classical bits than the number of qubits used, yet in some scenarios there are ways of conveying information with ...

We present a new protocol and two lower bounds for quantum coin flipping. In our protocol, no dishonest party can achieve one outcome with probability more than 0.75. Then, we show that our protocol is optimal for a certain type of quantum protocols.

For ...

An extractor is a procedure which extracts randomness from a detective random source using a few additional random bits. Explicit extractor constructions have numerous applications and obtaining such constructions is an important derandomization goal. ...

This paper introduces and explores a new condition based approach to solve the consensus problem in asynchronous systems. The approach consists of identifying sets of input vectors, called conditions, for which it is possible to design a protocol ...

The dynamic behavior of a network in which information is changing continuously over time requires robust and efficient mechanisms for keeping nodes updated about new information. Gossip protocols are mechanisms for this task in which nodes communicate ...

An (α,Β)-spanner of a graph G is a subgraph H such that d_H(u,w)\le α\cdot d_G(u,w)+Β for every pair of vertices u,w, where d_{G'}(u,w) denotes the distance between two vertices u and v in G'. It is known that every graph G has a polynomially ...

Let G=(V,E) be an undirected weighted graph with |V|=n and |E|=m. Let k\ge 1 be an integer. We show that G=(V,E) can be preprocessed in O(kmn^{1/k}) expected time, constructing a data structure of size O(kn^{1+1/k}), such that any subsequent distance ...

We define new error correcting codes based on extractors. We show that for certain choices of parameters these codes have better list decoding properties than are known for other codes, and are provably better than Reed-Solomon codes. We further show ...

We introduce a new construction of error-correcting codes from algebraic curves over finite fields. Modular curves of genus g\ra\infty over a field of size q_0^2 yield nonlinear codes more efficient than the linear Goppa codes obtained from the same ...

We consider a polynomial analogue of the hidden number problem which has recently been introduced by Boneh and Venkatesan. Namely we consider the sparse polynomial approximation problem of recovering an unknown polynomial f(X) \in \F_p[X] with at most $...

We present a randomized polynomial time algorithm to determine if a multivariate polynomial is zero using O(\log mnδ) random bits where n is the number of variables, m is the number of monomials, and δ is the total degree of the unknown polynomial. All ...

We show that we can maintain up to polylogarithmic edge connectivity for a fully-dynamic graph in \tilde O(\sqrt{n}) time per edge insertion or deletion. Within logarithmic factors, this matches the best time bound for 1-edge connectivity. Previously, ...

We show that for every fixed k\ge 0 there is a quadratic time algorithm that decides whether a given graph has crossing number at most k and, if this is the case, computes a drawing of the graph in the plane with at most k crossings.

Given a series-parallel graph, we consider the problem of drawing its layout in the plane (and the planar dual of the layout) such that the euler count of the layout is minimized. This problem is of considerable importance to the design of CMOS ...

We show that string graphs can be recognized in nondeterministic exponential time by giving an exponential upper bound on the number of intersections for a drawing realizing the string graph in the plane. This upper bound confirms a conjecture by ...

Mixtures of gaussian (or normal) distributions arise in a variety of application areas. Many techniques have been proposed for the task of finding the component gaussians given samples from the mixture, such as the EM algorithm, a local-search heuristic ...

Using techniques from learning theory, we show that any s-term DNF over n variables can be computed by a polynomial threshold function of degree O(n^{1/3} \log s). This upper bound matches, up to a logarithmic factor, the longstanding lower bound given ...