arXiv subjects

Vignesh Viswanathan

Publications and source records attributed to Vignesh Viswanathan.

25 records · Page 2Linked to original sources

arXiv2023

A General Framework for Fair Allocation under Matroid Rank Valuations

We study the problem of fairly allocating a set of indivisible goods among agents with matroid rank valuations -- every good provides a marginal value of $0$ or $1$ when added to a bundle and valuations are submodular. We generalize the Yankee Swap algorithm to create a simple framework, called General Yankee Swap, that can efficiently compute allocations that maximize any justice criterion (or fairness objective) satisfying some mild assumptions. Along with maximizing a justice criterion, General Yankee Swap is guaranteed to maximize utilitarian social welfare, ensure strategyproofness and use at most a quadratic number of valuation queries. We show how General Yankee Swap can be used to compute allocations for five different well-studied justice criteria: (a) Prioritized Lorenz dominance, (b) Maximin fairness, (c) Weighted leximin, (d) Max weighted Nash welfare, and (e) Max weighted $p$-mean welfare. In particular, our framework provides the first polynomial time algorithms to compute weighted leximin, max weighted Nash welfare and max weighted $p$-mean welfare allocations for agents with matroid rank valuations.

cs.GT↗

arXiv2023

Yankee Swap: a Fast and Simple Fair Allocation Mechanism for Matroid Rank Valuations

We study fair allocation of indivisible goods when agents have matroid rank valuations. Our main contribution is a simple algorithm based on the colloquial Yankee Swap procedure that computes provably fair and efficient Lorenz dominating allocations. While there exist polynomial time algorithms to compute such allocations, our proposed method improves on them in two ways. (a) Our approach is easy to understand and does not use complex matroid optimization algorithms as subroutines. (b) Our approach is scalable; it is provably faster than all known algorithms to compute Lorenz dominating allocations. These two properties are key to the adoption of algorithms in any real fair allocation setting; our contribution brings us one step closer to this goal.

cs.DS↗

arXiv2023

Weighted Notions of Fairness with Binary Supermodular Chores

We study the problem of allocating indivisible chores among agents with binary supermodular cost functions. In other words, each chore has a marginal cost of $0$ or $1$ and chores exhibit increasing marginal costs (or decreasing marginal utilities). In this note, we combine the techniques of Viswanathan and Zick (2022) and Barman et al. (2023) to present a general framework for fair allocation with this class of valuation functions. Our framework allows us to generalize the results of Barman et al. (2023) and efficiently compute allocations which satisfy weighted notions of fairness like weighted leximin or min weighted $p$-mean malfare for any $p \ge 1$.

cs.GT↗

arXiv2023

Learning Effective Strategies for Moving Target Defense with Switching Costs

Moving Target Defense (MTD) has emerged as a key technique in various security applications as it takes away the attacker's ability to perform reconnaissance for exploiting a system's vulnerabilities. However, most of the existing research in the field assumes unrealistic access to information about the attacker's motivations and/or actions when developing MTD strategies. Many of the existing approaches also assume complete knowledge regarding the vulnerabilities of a system and how each of these vulnerabilities can be exploited by an attacker. In this work, we aim to create algorithms that generate effective Moving Target Defense strategies that do not rely on prior knowledge about the attackers. Our work assumes that the only way the defender receives information about its own reward is via interaction with the attacker in a repeated game setting. Depending on the amount of information that can be obtained from the interactions, we devise two different algorithms using multi-armed bandit formulation to identify efficient strategies. We then evaluate our algorithms using data mined from the National Vulnerability Database to showcase that they match the performance of the state-of-the-art techniques, despite using a lot less amount of information.

cs.GT↗

arXiv2023

Relaxations of Envy-Freeness Over Graphs

When allocating a set of indivisible items among agents, the ideal condition of envy-freeness cannot always be achieved. Envy-freeness up to any good (EFX), and envy-freeness with $k$ hidden items (HEF-$k$) are two very compelling relaxations of envy-freeness, which remain elusive in many settings. We study a natural relaxation of these two fairness constraints, where we place the agents on the vertices of an undirected graph, and only require that our allocations satisfy the EFX (resp. HEF) constraint on the edges of the graph. We refer to these allocations as graph-EFX (resp. graph-HEF) or simply $G$-EFX (resp. $G$-HEF) allocations. We show that for any graph $G$, there always exists a $G$-HEF-$k$ allocation of goods, where $k$ is the size of a minimum vertex cover of $G$, and that this is essentially tight. We show that $G$-EFX allocations of goods exist for three different classes of graphs -- two of them generalizing the star $K_{1, n-1}$ and the third generalizing the three-edge path $P_4$. Many of these results extend to allocations of chores as well. Overall, we show several natural settings in which the graph structure helps obtain strong fairness guarantees. Finally, we evaluate an algorithm using problem instances from Spliddit to show that $G$-EFX allocations appear to exist for paths $P_n$, pointing the way towards showing EFX for even broader families of graphs.

cs.GT↗

arXiv2021

The Price is (Probably) Right: Learning Market Equilibria from Samples

Equilibrium computation in markets usually considers settings where player valuation functions are known. We consider the setting where player valuations are unknown; using a PAC learning-theoretic framework, we analyze some classes of common valuation functions, and provide algorithms which output direct PAC equilibrium allocations, not estimates based on attempting to learn valuation functions. Since there exist trivial PAC market outcomes with an unbounded worst-case efficiency loss, we lower-bound the efficiency of our algorithms. While the efficiency loss under general distributions is rather high, we show that in some cases (e.g., unit-demand valuations), it is possible to find a PAC market equilibrium with significantly better utility.

cs.GT↗

arXiv2013

Split-ball resonator

We introduce a new concept of split-ball resonator and demonstrate a strong magnetic dipole response for both gold and silver spherical plasmonic nanoparticles with nanometer-scale cuts. Tunability of the magnetic dipole resonance throughout the visible spectral range is demonstrated by changing the depth and width of the nanoscale cut. We realize this novel concept experimentally by employing the laser-induced transfer method to produce near-perfect spheres and helium ion beam milling to make cuts with the nanometer resolution. Due to high quality of the spherical particle shape governed by strong surface tension forces during the laser transfer process and clean, straight side walls of the cut made by helium ion milling, the magnetic resonance is observed at 600 nm in gold and at 565 nm in silver nanoparticles. Structuring arbitrary features on the surface of nanoscale spherical resonators provides new ways for engineering hybrid resonant modes and ultra-high near-field enhancement.

physics.optics↗