arXiv subjects

Haripriya Pulyassary

Publications and source records attributed to Haripriya Pulyassary.

7 recordsLinked to original sources

arXiv2026

Adaptive Sampling for Minimum-Norm $k$-Clustering

In $k$-clustering problems, we are given a metric space $(\mathcal{C}, d)$, and must choose a set $S$ of $k$ centers to open. Each client $j \in \mathcal{C}$ incurs an assignment cost, which is the distance between $j$ and center in $S$ that it has been assigned to. In this work, we study the \emph{minimum-norm $k$-clustering problem}, where we are given an arbitrary monotone symmetric norm $f$, and wish to open $k$ centers so as to minimize $f$(assignment-cost vector). This is a powerful generalization, encompassing many classical $k$-clustering problems including the $k$-median, $k$-means, and $k$-center problems. A simple and efficient algorithmic idea is that of \emph{adaptive sampling}, wherein we randomly choose the location of the next center to open with probability proportional to its ``cost" under the currently chosen set. While this has yielded fast algorithms for some $k$-clustering problem, little is known for settings \emph{without} ``min-sum" objectives. We devise the first adaptive-sampling-based bicriteria constant-factor approximation algorithm for general minimum-norm $k$-clustering, vastly expanding the scope of problems handled by adaptive sampling. For the special case of $\text{Top}_\ell$ norms, which form a building block of monotone symmetric norms, we show that adaptive sampling yields an $O(\log k)$-approximation algorithm.

cs.DS↗

arXiv2025

Market Design for Capacity Sharing in Networks

We study a market mechanism that sets edge prices to incentivize strategic agents to efficiently share limited network capacity. In this market, agents form coalitions, with each coalition sharing a unit capacity of a selected route and making payments to cover edge prices. Our focus is on the existence and computation of market equilibrium, where challenges arise from the interdependence between coalition formation among strategic agents with heterogeneous preferences and route selection that induces a network flow under integral capacity constraints. To address this interplay between coalition formation and network capacity utilization, we introduce a novel approach based on combinatorial auction theory and network flow theory. We establish sufficient conditions on the network topology and agents' preferences that guarantee both the existence and polynomial-time computation of a market equilibrium. Additionally, we identify a particular market equilibrium that maximizes utilities for all agents and the outcome is equivalent to the classical Vickrey-Clarke-Groves mechanism. Furthermore, we extend our results to multi-period settings and general networks, showing that when the sufficient conditions are not met, an equilibrium may still exist but requires more complex, path-based pricing mechanisms that set differentiated prices based on agents' preference parameters.

cs.GT↗

arXiv2025

Constant-Factor Distortion Mechanisms for $k$-Committee Election

In the $k$-committee election problem, we wish to aggregate the preferences of $n$ agents over a set of alternatives and select a committee of $k$ alternatives that minimizes the cost incurred by the agents. While we typically assume that agent preferences are captured by a cardinal utility function, in many contexts we only have access to ordinal information, namely the agents' rankings over the outcomes. As preference rankings are not as expressive as cardinal utilities, a loss of efficiency is inevitable, and is quantified by the notion of \emph{distortion}. We study the problem of electing a $k$-committee that minimizes the sum of the $\ell$-largest costs incurred by the agents, when agents and candidates are embedded in a metric space. This problem is called the $\ell$-centrum problem and captures both the utilitarian and egalitarian objectives. When $k \geq 2$, it is not possible to compute a bounded-distortion committee using purely ordinal information. We develop the first algorithms (that we call mechanisms) for the $\ell$-centrum problem (when $k \geq 2$), which achieve $O(1)$-distortion while eliciting only a very limited amount of cardinal information via value queries. We obtain two types of query-complexity guarantees: $O(\log k \log n)$ queries \emph{per agent}, and $O(k^2 \log^2 n)$ queries \emph{in total} (while achieving $O(1)$-distortion in both cases). En route, we give a simple adaptive-sampling algorithm for the $\ell$-centrum $k$-clustering problem.

cs.GT↗

arXiv2024

Capacity Allocation and Pricing of High Occupancy Toll Lane Systems with Heterogeneous Travelers

In this article, we study the optimal design of High Occupancy Toll (HOT) lanes. In our setup, the traffic authority determines the road capacity allocation between HOT lanes and ordinary lanes, as well as the toll price charged for travelers who use the HOT lanes but do not meet the high-occupancy eligibility criteria. We build a game-theoretic model to analyze the decisions made by travelers with heterogeneous values of time and carpool disutilities, who choose between paying or forming carpools to take the HOT lanes, or taking the ordinary lanes. Travelers' payoffs depend on the congestion cost of the lane that they take, the payment and the carpool disutilities. We provide a complete characterization of travelers' equilibrium strategies and resulting travel times for any capacity allocation and toll price. We also calibrate our model on the California Interstate highway 880 and compute the optimal capacity allocation and toll design.

cs.MA↗

arXiv2023

Network Flow Problems with Electric Vehicles

Electric vehicle (EV) adoption in long-distance logistics faces challenges such as range anxiety and uneven distribution of charging stations. Two pivotal questions emerge: How can EVs be efficiently routed in a charging network considering range limits, charging speeds and prices? And, can the existing charging infrastructure sustain the increasing demand for EVs in long-distance logistics? This paper addresses these questions by introducing a novel theoretical and computational framework to study the EV network flow problems. We present an EV network flow model that incorporates range constraints and nonlinear charging rates, and identify conditions under which polynomial-time solutions can be obtained for optimal single EV routing, maximum flow, and minimum-cost flow problems. Our findings provide insights for optimizing EV routing in logistics, ensuring an efficient and sustainable future.

cs.DS↗

arXiv2021

On the Randomized Metric Distortion Conjecture

In the single winner determination problem, we have n voters and m candidates and each voter j incurs a cost c(i, j) if candidate i is chosen. Our objective is to choose a candidate that minimizes the expected total cost incurred by the voters; however as we only have access to the agents' preference rankings over the outcomes, a loss of efficiency is inevitable. This loss of efficiency is quantified by distortion. We give an instance of the metric single winner determination problem for which any randomized social choice function has distortion at least 2.063164. This disproves the long-standing conjecture that there exists a randomized social choice function that has a worst-case distortion of at most 2.

cs.GT↗

arXiv2019

The Aggregation Closure is Polyhedral for Packing and Covering Integer Programs

Recently, Bodur, Del Pia, Dey, Molinaro and Pokutta introduced the concept of aggregation cuts for packing and covering integer programs. The aggregation closure is the intersection of all aggregation cuts. Bodur et. al. studied the strength of this closure, but left open the question of whether the aggregation closure is polyhedral. In this paper, we answer this question in the positive, i.e. we show that the aggregation closure is polyhedral. Finally, we demonstrate that a generalization, the k-aggregation closure, is also polyhedral for all k.

math.OC↗