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We show that the absolute value of the determinant of a matrix with random independent (but not necessarily i.i.d.) entries is strongly concentrated around its mean. As an application, we show that Godsil–Gutman and Barvinok estimators for the permanent of a strictly positive matrix give subexponential approximation ratios with high probability. A positive… (More)

We consider the following stochastic optimization problem first introduced by Chen et al. in [6]. We are given a vertex set of a random graph where each possible edge is present with probability pe. We do not know which edges are actually present unless we scan/probe an edge. However whenever we probe an edge and find it to be present, we are constrained to… (More)

We show that almost surely the rank of the adjacency matrix of the Erdös-Rényi random graph G(n, p) equals the number of non-isolated vertices for any c ln n/n < p < 1/2, where c is an arbitrary positive constant larger than 1/2. In particular the giant component (a.s.) has full rank in this range.

We consider the performance of two classic approximation algorithms which work by scanning the input and greedily constructing a solution. We investigate whether running these algorithms on a random permutation of the input can increase their performance ratio. We obtain the following results:
1. Johnson's approximation algorithm for MAX-SAT is one of the… (More)

We consider the following stochastic optimization problem first introduced by Chen et al. in [7]. We are given a vertex set of a random graph where each possible edge is present with probability pe. We do not know which edges are actually present unless we scan/probe an edge. However whenever we probe an edge and find it to be present, we are constrained to… (More)

We investigate the rank of random (symmetric) sparse matrices. Our main finding is that with high probability, any dependency that occurs in such a matrix is formed by a set of few rows that contains an overwhelming number of zeros. This allows us to obtain an exact estimate for the co-rank.

We study the problem of information gathering in ad-hoc radio networks without collision detection, focussing on the case when the network forms a tree, with edges directed towards the root. Initially, each node has a piece of information that we refer to as a rumor. Our goal is to design protocols that deliver all rumors to the root of the tree as quickly… (More)

Given fixed 0 = q0 < q1 < q2 < · · · < q k = 1 a constellation in [n] is a scaled translated realization of the qi with all elements in [n], i. We consider the problem of minimizing the number of monochromatic constellations in a two coloring of [n]. We show how given a coloring based on a block pattern how to find the number of monochromatic solutions to a… (More)

We study information gathering in ad-hoc radio networks. Initially, each node of the network has a piece of information called a rumor, and the overall objective is to gather all these rumors in the designated target node. The ad-hoc property refers to the fact that the topology of the network is unknown when the computation starts. Aggregation of rumors is… (More)

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