Pallavi Jain | IIT Jodhpur (original) (raw)

Papers by Pallavi Jain

Computers & Operations Research

Springer eBooks, 2023

In this paper, we study some multiagent variants of the knapsack problem. Fluschnik et al. [AAAI ... more 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.

Proceedings of the Genetic and Evolutionary Computation Conference Companion, 2017

Proceedings of the Genetic and Evolutionary Computation Conference Companion, 2018

In the last few years, parameterized complexity has emerged as a new tool to analyze the running ... more In the last few years, parameterized complexity has emerged as a new tool to analyze the running time of randomized local search algorithm. However, such analysis are few and far between. In this paper, we do a parameterized runtime analysis of a randomized local search algorithm and a (1 + 1) EA for a classical graph partitioning problem, namely, Max l-Uncut, and its balanced counterpart Max Balanced l-Uncut. In Max l-Uncut, given an undirected graph G = (V , E), the objective is to find a partition of V (G) into l parts such that the number of uncut edges-edges within the parts-is maximized. In the last few years, Max l-Uncut and Max Balanced l-Uncut are studied extensively from the approximation point of view. In this paper, we analyze the parameterized runtime of a randomized local search algorithm (RLS) for Max Balanced l-Uncut where the parameter is the number of uncut edges. RLS generates a solution of specific fitness in polynomial time for this problem. Furthermore, we design a fixed parameter tractable randomized local search and a (1 + 1) EA for Max l-Uncut and prove that they perform equally well.

Leibniz International Proceedings in Informatics, 2019

LIPIcs is a series of high-quality conference proceedings across all fields in informatics. LIPIc... more LIPIcs is a series of high-quality conference proceedings across all fields in informatics. LIPIcs volumes are published according to the principle of Open Access, i.e., they are available online and free of charge.

Liquid Democracy (LD) uses transitive delegations in voting. In its simplest form, it is used for... more Liquid Democracy (LD) uses transitive delegations in voting. In its simplest form, it is used for binary decisions, however its promise holds also for more advanced voting settings. Here we consider LD in the context of Participatory Budgeting (PB), which is a direct democracy approach to budgeting, most usually done in municipal budgeting processes. In particular, we study Knapsack Voting, in which PB voters approve projects, such that the sum of costs of projects each voter approves must respect the budget limit. We observe possible inconsistencies, as the cost of voter-approved projects may go over the budget limit after resolving delegations. We offer ways to overcome them by studying the computational complexity of updating as few delegations as possible to arrive— after following all project delegations—to a consistent profile.

Cryptographic algorithms, protocols, and applications are difficult to implement correctly, and e... more Cryptographic algorithms, protocols, and applications are difficult to implement correctly, and errors and vulnerabilities in their code can remain undiscovered for long periods before they are exploited. Even highly-regarded cryptographic libraries suffer from bugs like buffer overruns, incorrect numerical computations, and timing side-channels, which can lead to the exposure of sensitive data and longterm secrets. We describe a tool chain and framework based on the F∗ programming language to formally specify, verify and compile high-performance cryptographic software that is secure by design. This tool chain has been used to build a verified cryptographic library called HACL∗, and provably secure implementations of sophisticated secure communication protocols like Signal and TLS. We describe these case studies and conclude with ongoing work on using our framework to build verified implementations of privacy preserving machine learning software. 2012 ACM Subject Classification Secu...

ACM Transactions on Computation Theory, 2021

A graph operation that contracts edges is one of the fundamental operations in the theory of grap... more A graph operation that contracts edges is one of the fundamental operations in the theory of graph minors. Parameterized Complexity of editing to a family of graphs by contracting k edges has recently gained substantial scientific attention, and several new results have been obtained. Some important families of graphs, namely, the subfamilies of chordal graphs, in the context of edge contractions, have proven to be significantly difficult than one might expect. In this article, we study the F -Contraction problem, where F is a subfamily of chordal graphs, in the realm of parameterized approximation. Formally, given a graph G and an integer k , F -Contraction asks whether there exists X ⊆ E(G) such that G/X ∈ F and | X | ≤ k . Here, G/X is the graph obtained from G by contracting edges in X . We obtain the following results for the F - Contraction problem: • Clique Contraction is known to be FPT . However, unless NP⊆ coNP/ poly , it does not admit a polynomial kernel. We show that it...

d-Hitting Set and d-Set Cover are among the classical NP-hard problems. In this paper, we study v... more d-Hitting Set and d-Set Cover are among the classical NP-hard problems. In this paper, we study variants of d-Hitting Set and d-Set Cover, which are called Partial d -Hitting Set (Partial \(d\)-HS) and Partial \(d\)-Exact Set Cover (Partial \(d\)-Exact SC), respectively. In Partial \(d\)-HS, given a universe U, a family \({\mathcal F}\), of sets of size at most d over U, and integers k and t, the objective is to decide if there exists a \(S \subseteq U\) of size at most k such that S intersects with at least t sets in \(\mathcal {F}\). We obtain a kernel for Partial \(d\)-HS in which the size of the universe is bounded by \({\mathcal {O}}(dt)\) and the size of the family is bounded by \({\mathcal {O}}(dt^2)\). Using this result, we obtain a kernel for Partial Vertex Cover (PVC) with \({\mathcal {O}}(t)\) vertices, where t is the number of edges to be covered. Next, we study the Partial \(d\)-Exact SC problem, where, given a universe U, a family \({\mathcal F}\), of sets of size exac...

ArXiv, 2020

In the Stable Marriage problem. when the preference lists are complete, all agents of the smaller... more In the Stable Marriage problem. when the preference lists are complete, all agents of the smaller side can be matched. However, this need not be true when preference lists are incomplete. In most real-life situations, where agents participate in the matching market voluntarily and submit their preferences, it is natural to assume that each agent wants to be matched to someone in his/her preference list as opposed to being unmatched. In light of the Rural Hospital Theorem, we have to relax the "no blocking pair" condition for stable matchings in order to match more agents. In this paper, we study the question of matching more agents with fewest possible blocking edges. In particular, we find a matching whose size exceeds that of stable matching in the graph by at least t and has at most k blocking edges. We study this question in the realm of parameterized complexity with respect to several natural parameters, k,t,d, where d is the maximum length of a preference list. Unfor...

In this paper, we introduce a directed variant of the classical Bandwidth problem and study it fr... more In this paper, we introduce a directed variant of the classical Bandwidth problem and study it from the view-point of moderately exponential time algorithms, both exactly and approximately. Motivated by the definitions of the directed variants of the classical Cutwidth and Pathwidth problems, we define Digraph Bandwidth as follows. Given a digraph D and an ordering σ of its vertices, the digraph bandwidth of σ with respect to D is equal to the maximum value of σ(v)−σ(u) over all arcs (u, v) of D going forward along σ (that is, when σ(u) < σ(v)). The Digraph Bandwidth problem takes as input a digraph D and asks to output an ordering with the minimum digraph bandwidth. The undirected Bandwidth easily reduces to Digraph Bandwidth and thus, it immediately implies that Directed Bandwidth is NP-hard. While an O?(n!)1 time algorithm for the problem is trivial, the goal of this paper is to design algorithms for Digraph Bandwidth which have running times of the form 2O(n). In particular, ...

18 In this paper we study recently introduced conflict version of the classical Feedback Vertex 1... more 18 In this paper we study recently introduced conflict version of the classical Feedback Vertex 19 Set (FVS) problem. Let F be a family of graphs. Then, for every family F , we get F-CF20 Feedback Vertex Set (F-CF-FVS, for short). The problem F-CF-FVS takes as an input 21 a graph G, a graph H ∈ F , and an integer k, and the objective is to decide if there is a set 22 S ⊆ V (G) of size at most k such that G−S is a forest and S is an independent set in H. Observe 23 that if we instantiate F to be the family of edgeless graphs then we get the classical FVS problem. 24 Jain, Kanish and Misra [CSR 2018] showed that in contrast to FVS, F-CF-FVS is W[1]-hard 25 on general graphs and admits an FPT algorithm if F is a family of d-degenerate graphs. In 26 this paper we relate F-CF-FVS to the Independent Set problem on special classes of graphs 27 and obtain a complete dichotomy result on the Parameterized Complexity of the problem F28 CF-FVS. In particular, we show that F-CF-FVS is FPT parame...

A generalization of classical cycle hitting problems, called conflict version of the problem, is ... more A generalization of classical cycle hitting problems, called conflict version of the problem, is defined as follows. An input is undirected graphs G and H on the same vertex set, and a positive integer k, and the objective is to decide whether there exists a vertex subset X ⊆ V (G) such that it intersects all desired “cycles” (all cycles or all odd cycles or all even cycles) and X is an independent set in H. In this paper we study the conflict version of classical Feedback Vertex Set, and Odd Cycle Transversal problems, from the view point of kernelization complexity. In particular, we obtain the following results, when the conflict graph H belongs to the family of d-degenerate graphs. 1. CF-FVS admits a O(kO(d)) kernel. 2. CF-OCT does not admit polynomial kernel (even whenH is 1-degenerate), unless NP ⊆ coNP poly . For our kernelization algorithm we exploit ideas developed for designing polynomial kernels for the classical Feedback Vertex Set problem, as well as, devise new reducti...

Motivated by certain aggregation tasks related to participatory budgeting, such as clustering pro... more Motivated by certain aggregation tasks related to participatory budgeting, such as clustering projects and modeling project interactions, we study several variants of the following aggregation problem: Given a set P of m projects, and n partitions of P , the task is to aggregate these n partitions into one aggregated partition. We consider several aggregation methods for this setting, including utility-based methods and Condorcet-based methods and evaluate these methods by analyzing their computational complexity and their behavior with respect to certain relevant axiomatic properties.

Electronic Notes in Discrete Mathematics, 2017

Vertex Separation Minimization Problem (VSMP) consists of finding a layout of a graph G = (V, E) ... more Vertex Separation Minimization Problem (VSMP) consists of finding a layout of a graph G = (V, E) which minimizes the maximum vertex cut or separation of a layout. It is an NPcomplete problem in general for which metaheuristic techniques can be applied to find near optimal solution. VSMP has applications in VLSI design, graph drawing and computer language compiler design. VSMP is polynomially solvable for grids, trees, permutation graphs and cographs. Construction heuristics play a very important role in the metaheuristic techniques as they are responsible for generating initial solutions which lead to fast convergence. In this paper, we have proposed three construction heuristics H 1, H 2 and H 3 and performed experiments on Grids, Small graphs, Trees and Harwell Boeing graphs, totaling 248 instances of graphs. Experiments reveal that H 1, H 2 and H 3 are able to achieve best results for 88.71%, 43.5% and 37.1% of the total instances respectively while the best construction heuristic in the literature achieves the best solution for 39.9% of the total instances. We have also compared the results with the state-of-the-art metaheuristic GVNS and observed that the proposed construction heuristics improves the results for some of the input instances. It was found that GVNS obtained best results for 82.9% instances of all input instances and the heuristic H 1 obtained best results for 82.3% of all input instances.

Algorithmic Game Theory, 2021

The practice of partitioning a region into areas to favor a particular candidate or a party in an... more The practice of partitioning a region into areas to favor a particular candidate or a party in an election has been known to exist for the last two centuries. This practice is commonly known as gerrymandering. Recently, the problem has also attracted a lot of attention from complexity theory perspective. In particular, Cohen-Zemach et al. [AAMAS 2018] proposed a graph theoretic version of gerrymandering problem and initiated an algorithmic study around this, which was continued by Ito et al. [AAMAS 2019]. In this paper we continue this line of investigation and resolve an open problem in the literature, as well as move the algorithmic frontier forward by studying this problem in the realm of parameterized complexity. Our contributions in this article are twofold , conceptual and computational. We first resolve the open question posed by Ito et al. [AAMAS 2019] about the computational complexity of gerrymandering when the input graph is a path. Next, we propose a generalization of the model studied in [AAMAS 2019], where the input consists of a graph on n vertices representing the set of voters, a set of m candidates C, a weight function w v : C → Z + for each voter v ∈ V (G) representing the preference of the voter over the candidates, a distinguished candidate p ∈ C, and a positive integer k. The objective is to decide if it is possible to partition the vertex set into k districts (i.e., pairwise disjoint connected sets) such that the candidate p wins more districts than any other candidate. There are several natural parameters associated with the problem: the number of districts the vertex set needs to be partitioned (k), the number of voters (n), and the number of candidates (m). The problem is known to be NP-complete even if k = 2, m = 2, and G is either a complete bipartite graph (in fact K 2,n , a complete bipartite graphs with one side of size 2 and the other of size n) or a complete graph. This hardness result implies that we cannot hope to have an algorithm with running time (n + m) f (k,m) let alone f (k, m)(n + m) O(1) , where f is a function depending only on k and m, as this would imply that P=NP. This means that in search for FPT algorithms we need to either focus on the parameter n, or subclasses of forest (as the problem is NP-complete on K 2,n , a family of graphs that can be transformed into a forest by deleting one vertex). Circumventing these intractable results, we successfully obtain the following algorithmic results.

Theoretical Computer Science, 2020

Abstract A graph is called a split graph if its vertex set can be partitioned into a clique and a... more Abstract A graph is called a split graph if its vertex set can be partitioned into a clique and an independent set. Split graphs have rich mathematical structure and interesting algorithmic properties making it one of the most well-studied special graph classes. In the Split Vertex Deletion problem, given a graph and a positive integer k, the objective is to test whether there exists a subset of at most k vertices whose deletion results in a split graph. In this paper, we design a kernel for this problem with O ( k 2 ) vertices, improving upon the previous cubic bound known. Also, by giving a simple reduction from the Vertex Cover problem, we establish that Split Vertex Deletion does not admit a kernel with O ( k 2 − ϵ ) edges, for any ϵ > 0 , unless NP ⊆ coNP/poly .

Theory of Computing Systems, 2020

Let be a family of graphs. In the classical-VERTEX DELETION problem, given a graph G and a positi... more Let be a family of graphs. In the classical-VERTEX DELETION problem, given a graph G and a positive integer k, the objective is to check whether there exists a subset S of at most k vertices such that G − S is in. In this paper, we introduce the conflict free version of this classical problem, namely CONFLICT FREE-VERTEX DELETION (CF-VD), and study this problem from the viewpoint of classical and parameterized complexity. In the CF-VD problem, given two graphs G and H on the same vertex set and a positive integer k, the objective is to determine whether there exists a set S ⊆ V (G), of size at most k, such that G − S is in and H [S] is edgeless. Initiating a systematic study of these problems is one of the main conceptual contribution of this work. We obtain several results on the conflict free versions of several classical problems. Our first result shows that if is characterized by a finite family of forbidden induced subgraphs then CF-VD is Fixed Parameter Tractable (FPT). Furthermore, we obtain improved algorithms for conflict free versions of several well studied problems. Next, we show that if is characterized by a "well-behaved" infinite family of forbidden induced subgraphs, then CF-VD is W[1]-hard. Motivated by this hardness result, we consider the parameterized complexity of CF-VD when H is restricted to well studied families of graphs. In particular, we show that the conflict free version of several well-known problems such as FEEDBACK VERTEX SET, ODD CYCLE TRANSVERSAL, CHORDAL VER-TEX DELETION and INTERVAL VERTEX DELETION are FPT when H belongs to the families of d-degenerate graphs and nowhere dense graphs.

Algorithmica, 2020

An input to a conflict-free variant of a classical problem Γ, called Conflict-Free Γ, consists of... more An input to a conflict-free variant of a classical problem Γ, called Conflict-Free Γ, consists of an instance I of Γ coupled with a graph H, called the conflict graph. A solution to Conflict-Free Γ in (I, H) is a solution to I in Γ, which is also an independent set in H. In this paper, we study conflict-free variants of Maximum Matching and Shortest Path, which we call Conflict-Free Matching (CF-Matching) and Conflict-Free Shortest Path (CF-SP), respectively. We show that both CF-Matching and CF-SP are W[1]-hard, when parameterized by the solution size. Moreover, W[1]-hardness for CF-Matching holds even when the input graph where we want to find a matching is itself a matching, and W[1]-hardness for CF-SP holds for conflict graph being a unit-interval graph. Next, we study these problems with restriction on the conflict graphs. We give FPT algorithms for CF-Matching when the conflict graph is chordal. Also, we give FPT algorithms for both CF-Matching and CF-SP, when the conflict graph is d-degenerate. Finally, we design FPT algorithms for variants of CF-Matching and CF-SP, where the conflicting conditions are given by a (representable) matroid.

Autonomous Agents and Multi-Agent Systems, 2020

In a multiwinner election based on the Condorcet criterion, we are given a set of candidates, and... more In a multiwinner election based on the Condorcet criterion, we are given a set of candidates, and a set of voters with strict preference ranking over the candidates. A committee is weakly Gehrlein stable (WGS) if each committee member is preferred to each non-member by at least half of the voters. Recently, Aziz et al. [IJCAI 2017] studied the computational complexity of finding a WGS committee of size k. They show that this problem is NP-hard in general and polynomial time solvable when the number of voters is odd. In this article, we initiate a systematic study of the problem in the realm of parameterized complexity. We first show that the problem is W[1]-hard when parameterized by the size of the committee. To overcome this intractability result, we use a known reformulation of WGS as a problem on directed graphs and then use parameters that measure the "structure" of these directed graphs. In particular, we consider the majority graph, defined as follows: there is a vertex corresponding to each candidate, and there is a directed arc from a candidate c to c ′ if the number of voters that prefer c over c ′ is more than those that prefer c ′ over c. The problem of finding WGS committee of size k corresponds to finding a vertex subset X of size k in the majority graph with the following property: the set X contains no vertex outside the committee that has an in-neighbor in X. Observe that the polynomial time algorithm of Aziz et al. [IJCAI 2017] corresponds to solving the problem on a tournament (a complete graph with orientation on edges). Thus, natural parameters to study our problem are "closeness" to being a tournament. We define closeness as the number of missing arcs in the given directed graph and the number of vertices we need to delete from the given directed graph such that the resulting graph is a tournament. We show that the problem is fixed parameter tractable (FPT) and admits linear kernels with respect to closeness parameters. Finally, we also design an exact exponential time algorithm running in time O(1.2207 n n O(1)). Here, n denotes the number of candidates.