# Publications by Year: 2020

2020
Doron, Dean, Jack Murtagh, Salil Vadhan, and David Zuckerman. Spectral sparsification via bounded-independence sampling. Electronic Colloquium on Computational Complexity (ECCC), TR20-026, 2020. Publisher's VersionAbstract

Version History:

v1, 26 Feb 2020: https://arxiv.org/abs/2002.11237

We give a deterministic, nearly logarithmic-space algorithm for mild spectral sparsification of undirected graphs. Given a weighted, undirected graph $$G$$ on $$n$$ vertices described by a binary string of length $$N$$, an integer $$k \leq \log n$$ and an error parameter $$\varepsilon > 0$$, our algorithm runs in space $$\tilde{O}(k \log(N ^. w_{max}/w_{min}))$$ where $$w_{max}$$ and $$w_{min}$$ are the maximum and minimum edge weights in $$G$$, and produces a weighted graph $$H$$ with $$\tilde{O}(n^{1+2/k} / \varepsilon^2)$$expected edges that spectrally approximates $$G$$, in the sense of Spielmen and Teng [ST04], up to an error of $$\varepsilon$$.

Our algorithm is based on a new bounded-independence analysis of Spielman and Srivastava's effective resistance based edge sampling algorithm [SS08] and uses results from recent work on space-bounded Laplacian solvers [MRSV17]. In particular, we demonstrate an inherent tradeoff (via upper and lower bounds) between the amount of (bounded) independence used in the edge sampling algorithm, denoted by $$k$$ above, and the resulting sparsity that can be achieved.

Chen, Yiling, Or Sheffet, and Salil Vadhan. “Privacy games.” ACM Transactions on Economics and Computation 8, no. 2 (2020): Article 9. Publisher's VersionAbstract

Version History:

Previously published as: Yiling Chen, Or Sheffet, and Salil Vadhan. Privacy games. In Proceedings of the 10th International Conference on Web and Internet Economics (WINE ‘14), volume 8877 of Lecture Notes in Computer Science, pages 371–385. Springer-Verlag, 14–17 December 2014. (WINE Publisher's Version linked here: https://link.springer.com/chapter/10.1007/978-3-319-13129-0_30); PDF attached as WINE2014.

The problem of analyzing the effect of privacy concerns on the behavior of selfish utility-maximizing agents has received much attention lately. Privacy concerns are often modeled by altering the utility functions of agents to consider also their privacy loss. Such privacy aware agents prefer to take a randomized strategy even in very simple games in which non-privacy aware agents play pure strategies. In some cases, the behavior of privacy aware agents follows the framework of Randomized Response, a well-known mechanism that preserves differential privacy.

Our work is aimed at better understanding the behavior of agents in settings where their privacy concerns are explicitly given. We consider a toy setting where agent A, in an attempt to discover the secret type of agent B, offers B a gift that one type of B agent likes and the other type dislikes. As opposed to previous works, B's incentive to keep her type a secret isn't the result of "hardwiring" B's utility function to consider privacy, but rather takes the form of a payment between B and A. We investigate three different types of payment functions and analyze B's behavior in each of the resulting games. As we show, under some payments, B's behavior is very different than the behavior of agents with hardwired privacy concerns and might even be deterministic. Under a different payment we show that B's BNE strategy does fall into the framework of Randomized Response.