arXiv subjects

Palash Dey

Publications and source records attributed to Palash Dey.

At least 19 recordsLinked to original sources

arXiv2026

Fair, Efficient and Connected Allocations on Graphs

We study the classical and parameterized complexity of efficient connected allocation problems on graphs, where efficiency is measured by egalitarian and utilitarian welfare maximization. We first establish a sharp complexity dichotomy in the classical setting: both problems are NP-hard in general and remain hard even on very restricted graph classes such as paths, and consequently trees and cycles. In contrast, they are polynomial-time solvable on stars, but this tractability does not extend even to the case of two disjoint stars. Motivated by these boundaries, we move to the parameterized complexity framework, where we study the problem with respect to the number of agents. We obtain fixed-parameter tractability (FPT) on trees and, more generally, identify a robust phenomenon whereby tractability on a connected graph class extends to disjoint unions of graphs from that class. We further investigate the parameters treewidth and treedepth, showing that the utilitarian version is FPT for both, whereas the egalitarian version remains para-NP-hard even on graphs of treedepth two. Finally, we analyze the number of connected components and show that except for the collection of stars, the problems remain hard. For the collection of stars,while we obtain para-NP-hardness for the egalitarian case, the utilitarian case gives W[2]-hardness together with an XP algorithm.

cs.GT↗

arXiv2026

MLN-EIGS: A multilayer network framework for solving Stackelberg escape interdiction games on dynamic transportation networks

Interdicting an escaping criminal with limited police resources on large-scale transportation networks is a challenging problem due to the dynamic nature of both attacker movement and defender deployment. This paper proposes \emph{MLN-EIGS}, a multilayer network-based framework for solving dynamic escape interdiction problems formulated as a Stackelberg security game. A time-expanded multilayer network is constructed to explicitly model the temporal evolution of the transportation network and the feasible movements of both the attacker and the defenders. The attacker seeks to maximize the probability of successful escape, while the defenders aim to maximize the probability of interdiction. To efficiently compute the attacker's best response, the probabilistic escape formulation is transformed into an equivalent shortest-path problem through a logarithmic transformation, enabling the use of Dijkstra's algorithm. Since the defender best-response problem is computationally intractable, an approximation defender oracle is developed to generate high-quality defender strategies on the multilayer network. The proposed MLN-EIGS framework is benchmarked against an exact mixed-integer linear programming (MILP)-based Stackelberg formulation on a large real-world transportation network. Computational experiments demonstrate that MLN-EIGS consistently achieves defender utilities that closely match those of the exact MILP approach while substantially reducing computational time. These results demonstrate that the proposed MLN-EIGS framework provides an effective, computationally efficient, and scalable alternative to exact MILP-based Stackelberg optimization for large-scale dynamic escape interdiction problems.

cs.GT↗

arXiv2026

Parameterized Complexity of Finding a Maximum Common Vertex Subgraph Without Isolated Vertices

In this paper, we study the Maximum Common Vertex Subgraph problem: Given two input graphs $G_1,G_2$ and a non-negative integer $h$, is there a common subgraph $H$ on at least $h$ vertices such that there is no isolated vertex in $H$. In other words, each connected component of $H$ has at least $2$ vertices. This problem naturally arises in graph theory along with other variants of the well-studied Maximum Common Subgraph problem and also has applications in computational social choice. We show that this problem is NP-hard and provide an FPT algorithm when parameterized by $h$. Next, we conduct a study of the problem on common structural parameters like vertex cover number, maximum degree, treedepth, pathwidth and treewidth of one or both input graphs. We derive a complete dichotomy of parameterized results for our problem with respect to individual parameterizations as well as combinations of parameterizations from the above structural parameters. This provides us with a deep insight into the complexity theoretic and parameterized landscape of this problem.

cs.CC↗

arXiv2025

Kidney Exchange: Faster Parameterized Algorithms and Tighter Lower Bounds

The kidney exchange mechanism allows many patient-donor pairs who are otherwise incompatible with each other to come together and exchange kidneys along a cycle. However, due to infrastructure and legal constraints, kidney exchange can only be performed in small cycles in practice. In reality, there are also some altruistic donors who do not have any paired patients. This allows us to also perform kidney exchange along paths that start from some altruistic donor. Unfortunately, the computational task is NP-complete. To overcome this computational barrier, an important line of research focuses on designing faster algorithms, both exact and using the framework of parameterized complexity. The standard parameter for the kidney exchange problem is the number $t$ of patients that receive a healthy kidney. The current fastest known deterministic FPT algorithm for this problem, parameterized by $t$, is $O^\star\left(14^t\right)$. In this work, we improve this by presenting a deterministic FPT algorithm that runs in time $O^\star\left((4e)^t\right)\approx O^\star\left(10.88^t\right)$. This problem is also known to be W[1]-hard parameterized by the treewidth of the underlying undirected graph. A natural question here is whether the kidney exchange problem admits an FPT algorithm parameterized by the pathwidth of the underlying undirected graph. We answer this negatively in this paper by proving that this problem is W[1]-hard parameterized by the pathwidth of the underlying undirected graph. We also present some parameterized intractability results improving the current understanding of the problem under the framework of parameterized complexity.

cs.DS↗

arXiv2025

Fair Distribution of Digital Payments: Balancing Transaction Flows for Regulatory Compliance

The concentration of digital payment transactions in just two UPI apps like PhonePe and Google Pay has raised concerns of duopoly in India s digital financial ecosystem. To address this, the National Payments Corporation of India (NPCI) has mandated that no single UPI app should exceed 30 percent of total transaction volume. Enforcing this cap, however, poses a significant computational challenge: how to redistribute user transactions across apps without causing widespread user inconvenience while maintaining capacity limits? In this paper, we formalize this problem as the Minimum Edge Activation Flow (MEAF) problem on a bipartite network of users and apps, where activating an edge corresponds to a new app installation. The objective is to ensure a feasible flow respecting app capacities while minimizing additional activations. We further prove that Minimum Edge Activation Flow is NP-Complete. To address the computational challenge, we propose scalable heuristics, named Decoupled Two-Stage Allocation Strategy (DTAS), that exploit flow structure and capacity reuse. Experiments on large semi-synthetic transaction network data show that DTAS finds solutions close to the optimal ILP within seconds, offering a fast and practical way to enforce transaction caps fairly and efficiently.

cs.NI↗

arXiv2025

Shift Bribery over Social Networks

In shift bribery, a briber seeks to promote his preferred candidate by paying voters to raise their ranking. Classical models of shift bribery assume voters act independently, overlooking the role of social influence. However, in reality, individuals are social beings and are often represented as part of a social network, where bribed voters may influence their neighbors, thereby amplifying the effect of persuasion. We study Shift bribery over Networks, where voters are modeled as nodes in a directed weighted graph, and arcs represent social influence between them. In this setting, bribery is not confined to directly targeted voters its effects can propagate through the network, influencing neighbors and amplifying persuasion. Given a budget and individual cost functions for shifting each voter's preference toward a designated candidate, the goal is to determine whether a shift strategy exists within budget that ensures the preferred candidate wins after both direct and network-propagated influence takes effect. We show that the problem is NP-Complete even with two candidates and unit costs, and W[2]-hard when parameterized by budget or maximum degree. On the positive side, we design polynomial-time algorithms for complete graphs under plurality and majority rules and path graphs for uniform edge weights, linear-time algorithms for transitive tournaments for two candidates, linear cost functions and uniform arc weights, and pseudo-polynomial algorithms for cluster graphs. We further prove the existence of fixed-parameter tractable algorithms with treewidth as parameter for two candidates, linear cost functions and uniform arc weights and pseudo-FPT with cluster vertex deletion number for two candidates and uniform arc weights. Together, these results give a detailed complexity landscape for shift bribery in social networks.

cs.GT↗

arXiv2025

Minimizing Envy and Maximizing Happiness in Graphical House Allocation

We study the house allocation problem in a setting where agents are connected by a graph representing friendships. In this model, two agents can only envy each other if they are neighbors (i.e., friends) in the graph. Each agent has a set of preferred (liked) houses and dislikes the rest. An agent $a$ is said to envy a friend $b$ if $a$ is not assigned any house she likes, while $b$ is allocated a house that $a$ likes. This framework is known as graphical house allocation. Within this framework, we investigate two central problems. The first problem is to compute a house allocation that minimizes the number of envious agents. Multiple such allocations may exist that achieve the same minimum level of envy. Among all allocations that minimize envy, the second problem aims to find one that maximizes the number of agents who receive one of their preferred houses. We present a detailed complexity-theoretic analysis of these problems. In particular, we show that both problems can be solved in polynomial time when each agent prefers at most one house. However, both become NP-hard even when agents are allowed to prefer at most two houses, thereby highlighting the tight boundary between tractability and intractability. Additionally, we design exact algorithms for both problems under certain structural conditions on the agent graph, such as when the graph is sparse, has a small balanced separator, or admits a small vertex cover. These algorithms are significantly faster than the naive brute-force approach.

cs.DS↗

arXiv2025

Knapsack on Graphs with Relaxed Neighborhood Constraints

In the knapsack problems with neighborhood constraints that were studied before, the input is a graph $\mathcal{G}$ on a set $\mathcal{V}$ of items, each item $v \in \mathcal{V}$ has a weight $w_v$ and profit $p_v$, the size $s$ of the knapsack, and the demand $d$. The goal is to compute if there exists a feasible solution whose total weight is at most $s$ and total profit is at most $d$. Here, feasible solutions are all subsets $\mathcal{S}$ of the items such that, for every item in $\mathcal{S}$, at least one of its neighbors in $\mathcal{G}$ is also in $\mathcal{S}$ for \hor, and all its neighbors in $\mathcal{G}$ are also in $\mathcal{S}$ for \hand~\cite{borradaile2012knapsack}. We study a relaxation of the above problems. Specifically, we allow all possible subsets of items to be feasible solutions. However, only those items for which we pick at least one or all of its neighbor (out-neighbor for directed graph) contribute to profit whereas every item picked contribute to the weight; we call the corresponding problems \sor and \sand. We show that both \sor and \sand are strongly \NPC even on undirected graphs. Regarding parameterized complexity, we show both \sor and \hor are \WTH parameterized by the size $s$ of the knapsack size. Interestingly, both \sand and \hand are \WOH parameterized by knapsack size, $s$ plus profit demand, $d$ and also parameterized by solution size, $b$. For \sor and \hor, we present a randomized color-coding-based pseudo-\FPT algorithm, parameterized by the solution size $b$, and consequently by the demand $d$. We then consider the treewidth of the input graph as our parameter and design pseudo fixed-parameter tractable (\FPT) algorithm parameterized by treewidth, $\text{tw}$ for all variants. Finally, we present an additive $1$ approximation for \sor when both the weight and profit of every vertex is $1$.

cs.DS↗

arXiv2025

Maximizing Value in Challenge the Champ Tournaments

A tournament is a method to decide the winner in a competition, and describes the overall sequence in which matches between the players are held. While deciding a worthy winner is the primary goal of a tournament, a close second is to maximize the value generated for the matches played, with value for a match measured either in terms of tickets sold, television viewership, advertising revenue, or other means. Tournament organizers often seed the players -- i.e., decide which matches are played -- to increase this value. We study the value maximization objective in a particular tournament format called Challenge the Champ. This is a simple tournament format where an ordering of the players is decided. The first player in this order is the initial champion. The remaining players in order challenge the current champion; if a challenger wins, she replaces the current champion. We model the outcome of a match between two players using a complete directed graph, called a strength graph, with each player represented as a vertex, and the direction of an edge indicating the winner in a match. The value-maximization objective has been recently explored for knockout tournaments when the strength graph is a directed acyclic graph (DAG). We extend the investigation to Challenge the Champ tournaments and general strength graphs. We study different representations of the value of each match, and completely characterize the computational complexity of the problem.

cs.DS↗

arXiv2025

Projection-free Algorithms for Online Convex Optimization with Adversarial Constraints

We study a generalization of the Online Convex Optimization (OCO) framework with time-varying adversarial constraints. In this setting, at each round, the learner selects an action from a convex decision set $X$, after which both a convex cost function and a convex constraint function are revealed. The objective is to design a computationally efficient learning policy that simultaneously achieves low regret with respect to the cost functions and low cumulative constraint violation (CCV) over a horizon of length $T$. A major computational bottleneck in standard OCO algorithms is the projection operation onto the decision set $X$. However, for many structured decision sets, linear optimization can be performed efficiently. Motivated by this, we propose a projection-free online conditional gradient (OCG)-based algorithm that requires only a single call to a linear optimization oracle over $X$ per round. Our approach improves upon the state of the art for projection-free online learning with adversarial constraints, achieving $\tilde{O}(T^{\frac{3}{4}})$ bounds for both regret and CCV. Our algorithm is conceptually simple. It constructs a surrogate cost function as a nonnegative linear combination of the cost and constraint functions, and feeds these surrogate costs into a novel adaptive online conditional gradient subroutine introduced in this paper. We further extend our framework to the bandit setting, where we show that a new form of surrogate loss is necessary to properly handle bandit feedback - an issue overlooked in prior work. Finally, we develop an efficient Follow-the-Perturbed-Leader (FTPL)-based algorithm, particularly well-suited for online combinatorial optimization problems with discrete actions, which also achieves $O(T^{\frac{3}{4}})$ regret and CCV.

cs.LG↗

arXiv2024

Voter Participation Control in Online Polls

News outlets, surveyors, and other organizations often conduct polls on social networks to gain insights into public opinion. Such a poll is typically started by someone on a social network who sends it to her friends. If a person participates in the poll, the poll information gets published on her wall, which in turn enables her friends to participate, and the process continues. Eventually, a subset of the population participates in the poll, and the pollster learns the outcome of that poll. We initiate the study of a new but natural type of election control in such online elections. We study how difficult/easy it is to sway the outcome of such polls in one's favor/against (aka constructive vs destructive) by any malicious influencer who nudges/bribes people for seemingly harmless actions like non-participation. These questions are important from the standpoint of studying the power of resistance of online voting against malicious behavior. The destructive version is also important to quantify the robustness of the winner of an online voting. We show that both problems are computationally intractable even if the election is over only two candidates and the influencer has an infinite amount of money to spend (that is, every voter can be persuaded to not participate). We strengthen this result by proving that the computational task remains substantially challenging even if the underlying network is a tree. Finally, we show that there is a polynomial-time algorithm for the constructive version of the problem when we have O(1) candidates, and the treewidth of the underlying graph is O(1); the algorithm for the destructive version does not even need to assume O(1) number of candidates. Hence, we observe that the destructive version is computationally easier than the constructive version.

cs.MA↗

arXiv2024

Solving a Stackelberg Game on Transportation Networks in a Dynamic Crime Scenario: A Mixed Approach on Multi-Layer Networks

Interdicting a criminal with limited police resources is a challenging task as the criminal changes location over time. The size of the large transportation network further adds to the difficulty of this scenario. To tackle this issue, we consider the concept of a layered graph. At each time stamp, we create a copy of the entire transportation network to track the possible movements of both players, the attacker and the defenders. We consider a Stackelberg game in a dynamic crime scenario where the attacker changes location over time while the defenders attempt to interdict the attacker on his escape route. Given a set of defender strategies, the optimal attacker strategy is determined by applying Dijkstra's algorithm on the layered networks. Here, the attacker aims to minimize while the defenders aim to maximize the probability of interdiction. We develop an approximation algorithm on the layered networks to find near-optimal strategy for defenders. The efficacy of the developed approach is compared with the adopted MILP approach. We compare the results in terms of computational time and solution quality. The quality of the results demonstrates the need for the developed approach, as it effectively solves the complex problem within a short amount of time.

cs.AI↗

arXiv2024

Knapsack with Vertex Cover, Set Cover, and Hitting Set

Given an undirected graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$, with vertex weights $(w(u))_{u\in\mathcal{V}}$, vertex values $(\alpha(u))_{u\in\mathcal{V}}$, a knapsack size $s$, and a target value $d$, the \vcknapsack problem is to determine if there exists a subset $\mathcal{U}\subseteq\mathcal{V}$ of vertices such that $\mathcal{U}$ forms a vertex cover, $w(\mathcal{U})=\sum_{u\in\mathcal{U}} w(u) \le s$, and $\alpha(\mathcal{U})=\sum_{u\in\mathcal{U}} \alpha(u) \ge d$. In this paper, we closely study the \vcknapsack problem and its variations, such as \vcknapsackbudget, \minimalvcknapsack, and \minimumvcknapsack, for both general graphs and trees. We first prove that the \vcknapsack problem belongs to the complexity class \NPC and then study the complexity of the other variations. We generalize the problem to \setc and \hs versions and design polynomial time $H_g$-factor approximation algorithm for the \setckp problem and d-factor approximation algorithm for \hstp using primal dual method. We further show that \setcks and \hsmb are hard to approximate in polynomial time. Additionally, we develop a fixed parameter tractable algorithm running in time $8^{\mathcal{O}({\rm tw})}\cdot n\cdot {\sf min}\{s,d\}$ where ${\rm tw},s,d,n$ are respectively treewidth of the graph, the size of the knapsack, the target value of the knapsack, and the number of items for the \minimalvcknapsack problem.

cs.DS↗

arXiv2024

Query Complexity of Tournament Solutions

A directed graph where there is exactly one edge between every pair of vertices is called a {\em tournament}. Finding the "best" set of vertices of a tournament is a well studied problem in social choice theory. A {\em tournament solution} takes a tournament as input and outputs a subset of vertices of the input tournament. However, in many applications, for example, choosing the best set of drugs from a given set of drugs, the edges of the tournament are given only implicitly and knowing the orientation of an edge is costly. In such scenarios, we would like to know the best set of vertices (according to some tournament solution) by "querying" as few edges as possible. We, in this paper, precisely study this problem for commonly used tournament solutions: given an oracle access to the edges of a tournament T, find $f(T)$ by querying as few edges as possible, for a tournament solution f. We first show that the set of Condorcet non-losers in a tournament can be found by querying $2n-\lfloor \log n \rfloor -2$ edges only and this is tight in the sense that every algorithm for finding the set of Condorcet non-losers needs to query at least $2n-\lfloor \log n \rfloor -2$ edges in the worst case, where $n$ is the number of vertices in the input tournament. We then move on to study other popular tournament solutions and show that any algorithm for finding the Copeland set, the Slater set, the Markov set, the bipartisan set, the uncovered set, the Banks set, and the top cycle must query $Ω(n^2)$ edges in the worst case. On the positive side, we are able to circumvent our strong query complexity lower bound results by proving that, if the size of the top cycle of the input tournament is at most $k$, then we can find all the tournament solutions mentioned above by querying $O(nk + \frac{n\log n}{\log(1-\frac{1}{k})})$ edges only.

cs.DS↗

arXiv2024

Knapsack: Connectedness, Path, and Shortest-Path

We study the knapsack problem with graph theoretic constraints. That is, we assume that there exists a graph structure on the set of items of knapsack and the solution also needs to satisfy certain graph theoretic properties on top of knapsack constraints. In particular, we need to compute in the connected knapsack problem a connected subset of items which has maximum value subject to the size of knapsack constraint. We show that this problem is strongly NP-complete even for graphs of maximum degree four and NP-complete even for star graphs. On the other hand, we develop an algorithm running in time $O\left(2^{tw\log tw}\cdot\text{poly}(\min\{s^2,d^2\})\right)$ where $tw,s,d$ are respectively treewidth of the graph, size, and target value of the knapsack. We further exhibit a $(1-ε)$ factor approximation algorithm running in time $O\left(2^{tw\log tw}\cdot\text{poly}(n,1/ε)\right)$ for every $ε>0$. We show similar results for several other graph theoretic properties, namely path and shortest-path under the problem names path-knapsack and shortestpath-knapsack. Our results seems to indicate that connected-knapsack is computationally hardest followed by path-knapsack and shortestpath-knapsack.

cs.DS↗

arXiv2024

On Binary Networked Public Goods Game with Altruism

In the classical Binary Networked Public Goods (BNPG) game, a player can either invest in a public project or decide not to invest. Based on the decisions of all the players, each player receives a reward as per his/her utility function. However, classical models of BNPG game do not consider altruism which players often exhibit and can significantly affect equilibrium behavior. Yu et al. (2021) extended the classical BNPG game to capture the altruistic aspect of the players. We, in this paper, first study the problem of deciding the existence of a Pure Strategy Nash Equilibrium (PSNE) in a BNPG game with altruism. This problem is already known to be NP-Complete. We complement this hardness result by showing that the problem admits efficient algorithms when the input network is either a tree or a complete graph. We further study the Altruistic Network Modification problem, where the task is to compute if a target strategy profile can be made a PSNE by adding or deleting a few edges. This problem is also known to be NP-Complete. We strengthen this hardness result by exhibiting intractability results even for trees. A perhaps surprising finding of our work is that the above problem remains NP-Hard even for bounded degree graphs when the altruism network is undirected but becomes polynomial-time solvable when the altruism network is directed. We also show some results on computing an MSNE and some parameterized complexity results. In summary, our results show that it is much easier to predict how the players in a BNPG game will behave compared to how the players in a BNPG game can be made to behave in a desirable way.

cs.GT↗

arXiv2023

Evaluating District-based Election Surveys with Synthetic Dirichlet Likelihood

In district-based multi-party elections, electors cast votes in their respective districts. In each district, the party with maximum votes wins the corresponding seat in the governing body. Election Surveys try to predict the election outcome (vote shares and seat shares of parties) by querying a random sample of electors. However, the survey results are often inconsistent with the actual results, which could be due to multiple reasons. The aim of this work is to estimate a posterior distribution over the possible outcomes of the election, given one or more survey results. This is achieved using a prior distribution over vote shares, election models to simulate the complete election from the vote share, and survey models to simulate survey results from a complete election. The desired posterior distribution over the space of possible outcomes is constructed using Synthetic Dirichlet Likelihoods, whose parameters are estimated from Monte Carlo sampling of elections using the election models. We further show the same approach can also use be used to evaluate the surveys - whether they were biased or not, based on the true outcome once it is known. Our work offers the first-ever probabilistic model to analyze district-based election surveys. We illustrate our approach with extensive experiments on real and simulated data of district-based political elections in India.

stat.ME↗

arXiv2023

Parameterized Aspects of Distinct Kemeny Rank Aggregation

The Kemeny method is one of the popular tools for rank aggregation. However, computing an optimal Kemeny ranking is NP-hard. Consequently, the computational task of finding a Kemeny ranking has been studied under the lens of parameterized complexity with respect to many parameters. We first present a comprehensive relationship, both theoretical and empirical, among these parameters. Further, we study the problem of computing all distinct Kemeny rankings under the lens of parameterized complexity. We consider the target Kemeny score, number of candidates, average distance of input rankings, maximum range of any candidate, and unanimity width as our parameters. For all these parameters, we already have FPT algorithms. We find that any desirable number of Kemeny rankings can also be found without substantial increase in running time. We also present FPT approximation algorithms for Kemeny rank aggregation with respect to these parameters.

cs.DS↗