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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)

Consider a noisy linear observation model with an unknown permutation, based on observing $y = \Pi^* A x^* + w$, where $x^* \in \mathbb{R}^d$ is an unknown vector, $\Pi^*$ is an unknown $n \times n$ permutation matrix, and $w \in \mathbb{R}^n$ is additive Gaussian noise. We analyze the problem of permutation recovery in a random design setting in which the… (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)

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)

—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… (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)

—We consider the problem of maximizing the lifetime of coverage (MLCP) of targets in a wireless sensor network with battery-limited sensors. We first show that the MLCP cannot be approximated within a factor less than ln n by any polynomial time algorithm, where n is the number of targets. This provides closure to the long-standing open problem of showing… (More)

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