arXiv subjects

Neeldhara Misra

Publications and source records attributed to Neeldhara Misra.

44 records · Page 3Linked to original sources

arXiv2015

Detecting Possible Manipulators in Elections

Manipulation is a problem of fundamental importance in the context of voting in which the voters exercise their votes strategically instead of voting honestly to prevent selection of an alternative that is less preferred. The Gibbard-Satterthwaite theorem shows that there is no strategy-proof voting rule that simultaneously satisfies certain combinations of desirable properties. Researchers have attempted to get around the impossibility results in several ways such as domain restriction and computational hardness of manipulation. However these approaches have been shown to have limitations. Since prevention of manipulation seems to be elusive, an interesting research direction therefore is detection of manipulation. Motivated by this, we initiate the study of detection of possible manipulators in an election. We formulate two pertinent computational problems - Coalitional Possible Manipulators (CPM) and Coalitional Possible Manipulators given Winner (CPMW), where a suspect group of voters is provided as input to compute whether they can be a potential coalition of possible manipulators. In the absence of any suspect group, we formulate two more computational problems namely Coalitional Possible Manipulators Search (CPMS), and Coalitional Possible Manipulators Search given Winner (CPMSW). We provide polynomial time algorithms for these problems, for several popular voting rules. For a few other voting rules, we show that these problems are in NP-complete. We observe that detecting manipulation maybe easy even when manipulation is hard, as seen for example, in the case of the Borda voting rule.

cs.MA↗

arXiv2015

Kernelization Complexity of Possible Winner and Coalitional Manipulation Problems in Voting

In the Possible Winner problem in computational social choice theory, we are given a set of partial preferences and the question is whether a distinguished candidate could be made winner by extending the partial preferences to linear preferences. Previous work has provided, for many common voting rules, fixed parameter tractable algorithms for the Possible Winner problem, with number of candidates as the parameter. However, the corresponding kernelization question is still open and in fact, has been mentioned as a key research challenge. In this paper, we settle this open question for many common voting rules. We show that the Possible Winner problem for maximin, Copeland, Bucklin, ranked pairs, and a class of scoring rules that include the Borda voting rule do not admit a polynomial kernel with the number of candidates as the parameter. We show however that the Coalitional Manipulation problem which is an important special case of the Possible Winner problem does admit a polynomial kernel for maximin, Copeland, ranked pairs, and a class of scoring rules that includes the Borda voting rule, when the number of manipulators is polynomial in the number of candidates. A significant conclusion of our work is that the Possible Winner problem is harder than the Coalitional Manipulation problem since the Coalitional Manipulation problem admits a polynomial kernel whereas the Possible Winner problem does not admit a polynomial kernel.

cs.GT↗

arXiv2014

Vertex Cover Gets Faster and Harder on Low Degree Graphs

The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric objects, often turns out to be exactly the vertex cover problem on restricted classes of graphs. In this work we explore a particular instance of such a phenomenon. We consider the problem of hitting all axis-parallel slabs induced by a point set P, and show that it is equivalent to the problem of finding a vertex cover on a graph whose edge set is the union of two Hamiltonian Paths. We show the latter problem to be NP-complete, and we also give an algorithm to find a vertex cover of size at most k, on graphs of maximum degree four, whose running time is 1.2637^k n^O(1).

cs.DS↗

arXiv2013

On the Parameterized Complexity of the Maximum Edge Coloring Problem

We investigate the parameterized complexity of the following edge coloring problem motivated by the problem of channel assignment in wireless networks. For an integer q>1 and a graph G, the goal is to find a coloring of the edges of G with the maximum number of colors such that every vertex of the graph sees at most q colors. This problem is NP-hard for q>1, and has been well-studied from the point of view of approximation. Our main focus is the case when q=2, which is already theoretically intricate and practically relevant. We show fixed-parameter tractable algorithms for both the standard and the dual parameter, and for the latter problem, the result is based on a linear vertex kernel.

cs.DS↗

arXiv2013

Upper and Lower Bounds for Weak Backdoor Set Detection

We obtain upper and lower bounds for running times of exponential time algorithms for the detection of weak backdoor sets of 3CNF formulas, considering various base classes. These results include (omitting polynomial factors), (i) a 4.54^k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Horn formulas; (ii) a 2.27^k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Krom formulas. These bounds improve an earlier known bound of 6^k. We also prove a 2^k lower bound for these problems, subject to the Strong Exponential Time Hypothesis.

cs.DS↗

arXiv2013

An Erdős--Ko--Rado theorem for matchings in the complete graph

We consider the following higher-order analog of the Erdős--Ko--Rado theorem. For positive integers r and n with r<= n, let M^r_n be the family of all matchings of size r in the complete graph K_{2n}. For any edge e in E(K_{2n}), the family M^r_n(e), which consists of all sets in M^r_n containing e, is called the star centered at e. We prove that if r<n and A is an intersecting family of matchings in M^r_n, then |A|<=|M^r_n(e)|$, where e is an edge in E(K_{2n}). We also prove that equality holds if and only if A is a star. The main technique we use to prove the theorem is an analog of Katona's elegant cycle method.

math.CO↗

arXiv2010

Hitting forbidden minors: Approximation and Kernelization

We study a general class of problems called F-deletion problems. In an F-deletion problem, we are asked whether a subset of at most $k$ vertices can be deleted from a graph $G$ such that the resulting graph does not contain as a minor any graph from the family F of forbidden minors. We obtain a number of algorithmic results on the F-deletion problem when F contains a planar graph. We give (1) a linear vertex kernel on graphs excluding $t$-claw $K_{1,t}$, the star with $t$ leves, as an induced subgraph, where $t$ is a fixed integer. (2) an approximation algorithm achieving an approximation ratio of $O(\log^{3/2} OPT)$, where $OPT$ is the size of an optimal solution on general undirected graphs. Finally, we obtain polynomial kernels for the case when F contains graph $θ_c$ as a minor for a fixed integer $c$. The graph $θ_c$ consists of two vertices connected by $c$ parallel edges. Even though this may appear to be a very restricted class of problems it already encompasses well-studied problems such as {\sc Vertex Cover}, {\sc Feedback Vertex Set} and Diamond Hitting Set. The generic kernelization algorithm is based on a non-trivial application of protrusion techniques, previously used only for problems on topological graph classes.

cs.DS↗

arXiv2009

FPT Algorithms for Connected Feedback Vertex Set

We study the recently introduced Connected Feedback Vertex Set (CFVS) problem from the view-point of parameterized algorithms. CFVS is the connected variant of the classical Feedback Vertex Set problem and is defined as follows: given a graph G=(V,E) and an integer k, decide whether there exists a subset F of V, of size at most k, such that G[V F] is a forest and G[F] is connected. We show that Connected Feedback Vertex Set can be solved in time $O(2^{O(k)}n^{O(1)})$ on general graphs and in time $O(2^{O(\sqrt{k}\log k)}n^{O(1)})$ on graphs excluding a fixed graph H as a minor. Our result on general undirected graphs uses as subroutine, a parameterized algorithm for Group Steiner Tree, a well studied variant of Steiner Tree. We find the algorithm for Group Steiner Tree of independent interest and believe that it will be useful for obtaining parameterized algorithms for other connectivity problems.

cs.DS↗