Ashwin Pananjady

Learn More
We consider the problem of a social group of users trying to obtain a " universe " of files, first from a server and then via exchange amongst themselves. We consider the selfish file-exchange paradigm of give-and-take, whereby two users can exchange files only if each has something unique to offer the other. We are interested in maximizing the number of(More)
We establish quantitative stability results for the entropy power inequality (EPI). Specifically, we show that if uniformly log-concave densities nearly saturate the EPI, then they must be close to Gaussian densities in the quadratic Wasserstein distance. Further, if one of the densities is log-concave and the other is Gaussian, then the deficit in the EPI(More)
Consider a noisy linear observation model with an unknown permutation, based on observing y = &#x03A0;*Ax* + w, where x* &#x2208; &#x211D;<sup>d</sup> is an unknown vector, &#x03A0;* is an unknown n &#x00D7; n permutation matrix, and w &#x2208; &#x211D;<sup>n</sup> is additive Gaussian noise. We analyze the problem of permutation recovery in a random design(More)
We consider a variable-length source coding problem subject to local decodability constraints. In particular, we investigate the blocklength scaling behavior attainable by encodings of r-sparse binary sequences, under the constraint that any source bit can be correctly decoded upon probing at most d codeword bits. We consider both adaptive and non-adaptive(More)
We address a classical problem concerning energy efficiency in sensor networks. In particular, we consider the problem of maximizing the lifetime of coverage of targets in a wireless sensor network with battery-limited sensors. We first show that the problem cannot be approximated within a factor less than <inline-formula> <tex-math notation="LaTeX">$\ln n$(More)
In this paper, we investigate the approximability of two node deletion problems. Given a vertex weighted graph G = (V, E) and a specified, or " distinguished " vertex p ∈ V , MDD(min) is the problem of finding a minimum weight vertex set S ⊆ V \ {p} such that p becomes the minimum degree vertex in G[V \ S]; and MDD(max) is the problem of finding a minimum(More)
We establish existence of Stein kernels for probability measures on R d satisfying a Poincaré inequality, and obtain bounds on the Stein discrepancy of such measures. Applications to quantitative central limit theorems are discussed, including a new CLT in Wasserstein distance W 2 with optimal rate and dependence on the dimension. As a byproduct, we obtain(More)
The integrality gap of the integer programming formulation of the maximum lifetime coverage problem (or equivalently, the LP formulation of the cover decomposition problem, also known as the disjoint set cover problem (DSCP)) was conjectured to be 2 in [4]. This is a special case of the packing LP, which in the general case has an unbounded integrality gap.(More)
Given a universe U of n elements and a collection of subsets S of U, the maximum disjoint set cover problem (DSCP) is to partition S into as many set covers as possible, where a set cover is defined as a collection of subsets whose union is U. We consider the online DSCP, in which the subsets arrive one by one (possibly in an order chosen by an adversary),(More)
  • 1