Kevin P. Costello

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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 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)
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 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)
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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