Srinivasan Venkatesh

On the advantage over a random assignment

We initiate the study of a new measure of approximation. This measure compares the performance of an approximation algorithm to the random assignment algorithm. This is a useful measure for optimization problems where the random assignment algorithm is known to give essentially the best possible polynomial time approximation. In this paper, we focus on this measure for the optimization problems Max-Lin-2 in which we need to maximize the number of satisfied linear equations in a system of linear equations modulo 2, and Max-k-Lin-2, a special case of the above problem in which each equation has at most k variables. The main techniques we use, in our approximation algorithms and inapproximability results for this measure, are from Fourier analysis and derandomization.

The Communication Complexity of Pointer Chasing

We study the k-round two-party communication complexity of the pointer chasing problem for fixed k. C. Damm, S. Jukna and J. Sgall (1998, Comput. Complexity7, 109?127) showed an upper bound of O(nlog(k?1)n) for this problem. We prove a matching lower bound; this improves the lower bound of ?(n) shown by N. Nisan and A. Widgerson (1993, SIAM J. Comput.22, 211?219), and yields a corresponding improvement in the hierarchy results derived by them and by H. Klauck (1998, in “Proceeding of the Thirteenth Annual IEEE Conference on Computational Complexity,” pp. 141?152) for bounded-depth monotone circuits. We consider the bit version of this problem, and show upper and lower bounds. This implies that there is an abrupt jump in complexity, from linear to superlinear, when the number of rounds is reduced to k/2 or less. We also consider the s-paths version (originally studied by H. Klauck) and show an upper bound. The lower bounds are based on arguments using entropy. One of the main contributions of this work is a transfer lemma for distributions with high entropy; this should be of independent interest.

Improved bounds for dictionary look-up with one error

Abstract Given a dictionary S of n binary strings each of length m , we consider the problem of designing a data structure for S that supports d -queries; given a binary query string q of length m , a d -query reports if there exists a string in S within Hamming distance d of q . We construct a data structure for the case d=1 , that requires space O (n log m) and has query time O (1) in a cell probe model with word size m . This generalizes and improves the previous bounds of Yao and Yao for the problem in the bit probe model. The data structure can be constructed in randomized expected time O (nm) .

Social Network Anonymization via Edge Addition

The growing need to address privacy concerns when social network data is released for mining purposes has recently led to considerable interest in various techniques for graph anonymization. In this paper, we study the following problem: Given a social network modeled as an {\em edge-labeled graph}

Anonymizing Subsets of Social Networks with Degree Constrained Subgraphs

G

Visibly pushdown transducers for approximate validation of streaming XML

, we aim to make a pre-specified subset of vertices of

Computing k-regret minimizing sets

G

Approximating the Radii of Point Sets

k

On approximating the radii of point sets in high dimensions

-label sequence anonymous with the minimum number of edge additions. Here, the label sequence of a vertex is the sequence of labels of edges incident to it. The contributions of this paper are two fold: We provide a framework to show hardness results for different variants of social network anonymization using a common approach. We start by showing that