arXiv subjects

Sanjay Seetharaman

Publications and source records attributed to Sanjay Seetharaman.

10 recordsLinked to original sources

arXiv2026

On the Hardness of Maximin Share Allocations

The maximin share (MMS) guarantee is a central fairness benchmark for allocating indivisible items. Since Kurokawa, Procaccia and Wang [EC'14, JACM'18] showed that exact MMS allocations need not exist, much work has studied existence and computation of approximate MMS allocations. In contrast, a basic complexity question posed more than a decade ago by Bouveret and Lemaître [JAAMAS'16] has remained unresolved: how hard is it to decide whether an exact MMS allocation exists? For additive valuations, Lonc and Truszczynski [JAIR'20] showed membership in $Δ_2^P$ (also known as $P^{NP}$), but no hardness result was known. For the more general class of 2-additive valuations, Bouveret and Lemaître established NP-hardness, leaving a substantial gap to the $Δ_2^P$ upper bound. Moreover, the (precise) complexity of MMS existence in additive and $k$-additive settings was posed as an open question. We make progress on all of these fronts: (1) For additive goods, we prove that deciding MMS existence is $D^P$-hard, giving the first hardness result for this longstanding problem. (2) For 2-additive valuations, we close the complexity gap by proving $Δ_2^P$-completeness on a class of instances of monotone submodular goods. To the best of our knowledge this is the first result of this kind. We also prove weak coNP-hardness for three agents, thereby establishing a precise dichotomy with the known existence guarantee for two agents; and strong coNP-hardness when the number of agents is unrestricted. Moreover, the strong hardness construction produces an inverse-polynomial gap in the optimal MMS approximation ratio, ruling out an FPTAS for approximating this ratio unless P=NP. Finally, we show that all these results for goods extend to the chores setting through a polynomial-time transformation that preserves MMS existence.

cs.GT↗

arXiv2026

A Simple Algorithm for Combinatorial n-Fold ILPs Using the Steinitz Lemma

We present an algorithm for a class of $n$-fold ILPs whose existing algorithms in literature are often either (1) based on the \textit{augmentation framework} where one starts with an arbitrary solution and then iteratively moves towards an optimal solution by solving appropriate programs; or (2) require solving a linear relaxation of the program; or (3) are based on decomposition/proximity based arguments. Combinatorial $n$-fold ILPs is a class of $n$-fold ILPs introduced and studied by Knop et al. [MP2020] that captures several other problems in a variety of domains. We present a simple and direct algorithm that solves combinatorial $n$-fold ILPs with unbounded non-negative variables via an application of the Steinitz lemma. Depending on the structure of the input ILP, we also improve upon the existing algorithms in the literature in terms of the running time, thereby showing an improvement that mirrors the one shown by Rohwedder [ICALP2025] contemporaneously and independently.

cs.DS↗

arXiv2026

Dominating Set with Quotas: Balancing Coverage and Constraints

We study a natural generalization of the classical \textsc{Dominating Set} problem, called \textsc{Dominating Set with Quotas} (DSQ). In this problem, we are given a graph $ G $, an integer $ k $, and for each vertex $ v \in V(G) $, a lower quota $ \mathrm{lo}_v $ and an upper quota $ \mathrm{up}_v $. The goal is to determine whether there exists a set $ S \subseteq V(G) $ of size at most $ k $ such that for every vertex $ v \in V(G) $, the number of vertices in its closed neighborhood that belong to $ S $, i.e., $ |N[v] \cap S| $, lies within the range $ [\mathrm{lo}_v, \mathrm{up}_v] $. This richer model captures a variety of practical settings where both under- and over-coverage must be avoided -- such as in fault-tolerant infrastructure, load-balanced facility placement, or constrained communication networks. While DS is already known to be computationally hard, we show that the added expressiveness of per-vertex quotas in DSQ introduces additional algorithmic challenges. In particular, we prove that DSQ becomes \W[1]-hard even on structurally sparse graphs -- such as those with degeneracy 2, or excluding $ K_{3,3} $ as a subgraph -- despite these classes admitting FPT algorithms for DS. On the positive side, we show that DSQ is fixed-parameter tractable when parameterized by solution size and treewidth, and more generally, on nowhere dense graph classes. Furthermore, we design a subexponential-time algorithm for DSQ on apex-minor-free graphs using the bidimensionality framework. These results collectively offer a refined view of the algorithmic landscape of DSQ, revealing a sharp contrast with the classical DS problem and identifying the key structural properties that govern tractability.

cs.DS↗

arXiv2026

Line Cover and Related Problems

We study extensions of the classic \emph{Line Cover} problem, which asks whether a set of $n$ points in the plane can be covered using $k$ lines. Line Cover is known to be NP-hard, and we focus on two natural generalizations. The first is \textbf{Line Clustering}, where the goal is to find $k$ lines minimizing the sum of squared distances from the input points to their nearest line. The second is \textbf{Hyperplane Cover}, which asks whether $n$ points in $\mathbb{R}^d$ can be covered by $k$ hyperplanes. We also study the more general \textbf{Projective Clustering} problem, which unifies both settings and has applications in machine learning, data analysis, and computational geometry. In this problem, one seeks $k$ affine subspaces of dimension $r$ that minimize the sum of squared distances from the given points in $\mathbb{R}^d$ to the nearest subspace. Our results reveal notable differences in the parameterized complexity of these problems. While Line Cover is fixed-parameter tractable when parameterized by $k$, we show that Line Clustering is W[1]-hard with respect to $k$ and does not admit an algorithm with running time $n^{o(k)}$ unless the Exponential Time Hypothesis fails. Hyperplane Cover has been known to be NP-hard since the 1980s, following work of Megiddo and Tamir, even for $d=2$, we show that it remains NP-hard even when $k=2$. Finally, we present an algorithm for Projective Clustering running in $n^{O(dk(r+1))}$ time. This bound matches our lower bound for Line Clustering and generalizes the classic algorithm for $k$-Means Clustering ($r=0$) by Inaba, Katoh, and Imai [SoCG 1994].

cs.CG↗

arXiv2026

Robust Value Maximization in Challenge the Champ Tournaments with Probabilistic Outcomes

Challenge the Champ is a simple tournament format, where an ordering of the players -- called a seeding -- is decided. The first player in this order is the initial champ, and faces the next player. The outcome of each match decides the current champion, who faces the next player in the order. Each player also has a popularity, and the value of each match is the popularity of the winner. Value maximization in tournaments has been previously studied when each match has a deterministic outcome. However, match outcomes are often probabilistic, rather than deterministic. We study robust value maximization in Challenge the Champ tournaments, when the winner of a match may be probabilistic. That is, we seek to maximize the total value that is obtained, irrespective of the outcome of probabilistic matches. We show that even in simple binary settings, for non-adaptive algorithms, the optimal robust value -- which we term the \textsc{VnaR}, or the value not at risk -- is hard to approximate. However, if we allow adaptive algorithms that determine the order of challengers based on the outcomes of previous matches, or restrict the matches with probabilistic outcomes, we can obtain good approximations to the optimal \textsc{VnaR}.

cs.GT↗

arXiv2026

When agents choose bundles autonomously: guarantees beyond discrepancy

We consider the fair division of indivisible items among $n$ agents with additive non-negative normalized valuations, with the goal of obtaining high value guarantees, that is, close to the proportional share for each agent. We prove that partitions where \emph{every} part yields high value for each agent are asymptotically limited by a discrepancy barrier of $Θ(\sqrt{n})$. Guided by this, our main objective is to overcome this barrier and achieve stronger individual guarantees for each agent in polynomial time. Towards this, we are able to exhibit an exponential improvement over the discrepancy barrier. In particular, we can create partitions on-the-go such that when agents arrive sequentially (representing a previously-agreed priority order) and pick a part autonomously and rationally (i.e., one of highest value), then each is guaranteed a part of value at least $\mathsf{PROP} - \mathcal{O}{(\log n)}$. Moreover, we show even better guarantees for three restricted valuation classes such as those defined by: a common ordering on items, a bound on the multiplicity of values, and a hypergraph with a bound on the \emph{influence} of any agent. Specifically, we study instances where: (1) the agents are ``close'' to unanimity in their relative valuation of the items -- a generalization of the ordered additive setting; (2) the valuation functions do not assign the same positive value to more than $t$ items; and (3) the valuation functions respect a hypergraph, a setting introduced by Christodoulou et al. [EC'23], where agents are vertices and items are hyperedges. While the sizes of the hyperedges and neighborhoods can be arbitrary, the influence of any agent $a$, defined as the number of its neighbors who value at least one item positively that $a$ also values positively, is bounded.

cs.GT↗

arXiv2024

Quick-Sort Style Approximation Algorithms for Generalizations of Feedback Vertex Set in Tournaments

A feedback vertex set (FVS) in a digraph is a subset of vertices whose removal makes the digraph acyclic. In other words, it hits all cycles in the digraph. Lokshtanov et al. [TALG '21] gave a factor 2 randomized approximation algorithm for finding a minimum weight FVS in tournaments. We generalize the result by presenting a factor $2α$ randomized approximation algorithm for finding a minimum weight FVS in digraphs of independence number $α$; a generalization of tournaments which are digraphs with independence number $1$. Using the same framework, we present a factor $2$ randomized approximation algorithm for finding a minimum weight Subset FVS in tournaments: given a vertex subset $S$ in addition to the graph, find a subset of vertices that hits all cycles containing at least one vertex in $S$. Note that FVS in tournaments is a special case of Subset FVS in tournaments in which $S = V(T)$.

cs.DS↗

arXiv2022

More Effort Towards Multiagent Knapsack

In this paper, we study some multiagent variants of the knapsack problem. Fluschnik et al. [AAAI 2019] considered the model in which every agent assigns some utility to every item. They studied three preference aggregation rules for finding a subset (knapsack) of items: individually best, diverse, and Nash-welfare-based. Informally, diversity is achieved by satisfying as many voters as possible. Motivated by the application of aggregation operators in multiwinner elections, we extend the study from diverse aggregation rule to Median and Best scoring functions. We study the computational and parameterized complexity of the problem with respect to some natural parameters, namely, the number of voters, the number of items, and the distance from an easy instance. We also study the complexity of the problem under domain restrictions. Furthermore, we present significantly faster parameterized algorithms with respect to the number of voters for the diverse aggregation rule.

cs.GT↗

arXiv2021

Gradient-based Data Subversion Attack Against Binary Classifiers

Machine learning based data-driven technologies have shown impressive performances in a variety of application domains. Most enterprises use data from multiple sources to provide quality applications. The reliability of the external data sources raises concerns for the security of the machine learning techniques adopted. An attacker can tamper the training or test datasets to subvert the predictions of models generated by these techniques. Data poisoning is one such attack wherein the attacker tries to degrade the performance of a classifier by manipulating the training data. In this work, we focus on label contamination attack in which an attacker poisons the labels of data to compromise the functionality of the system. We develop Gradient-based Data Subversion strategies to achieve model degradation under the assumption that the attacker has limited-knowledge of the victim model. We exploit the gradients of a differentiable convex loss function (residual errors) with respect to the predicted label as a warm-start and formulate different strategies to find a set of data instances to contaminate. Further, we analyze the transferability of attacks and the susceptibility of binary classifiers. Our experiments show that the proposed approach outperforms the baselines and is computationally efficient.

cs.LG↗

arXiv2021

Influence Based Defense Against Data Poisoning Attacks in Online Learning

Data poisoning is a type of adversarial attack on training data where an attacker manipulates a fraction of data to degrade the performance of machine learning model. Therefore, applications that rely on external data-sources for training data are at a significantly higher risk. There are several known defensive mechanisms that can help in mitigating the threat from such attacks. For example, data sanitization is a popular defensive mechanism wherein the learner rejects those data points that are sufficiently far from the set of training instances. Prior work on data poisoning defense primarily focused on offline setting, wherein all the data is assumed to be available for analysis. Defensive measures for online learning, where data points arrive sequentially, have not garnered similar interest. In this work, we propose a defense mechanism to minimize the degradation caused by the poisoned training data on a learner's model in an online setup. Our proposed method utilizes an influence function which is a classic technique in robust statistics. Further, we supplement it with the existing data sanitization methods for filtering out some of the poisoned data points. We study the effectiveness of our defense mechanism on multiple datasets and across multiple attack strategies against an online learner.

cs.LG↗