• B-chromatic number: Beyond NP-hardness 

      Panolan, Fahad; Philip, Geevarghese; Saurabh, Saket (Conference object; Peer reviewed; Journal article, 2015)
      The b-chromatic number of a graph G, chi_b(G), is the largest integer k such that G has a k-vertex coloring with the property that each color class has a vertex which is adjacent to at least one vertex in each of the other ...
    • Balanced judicious bipartition is fixed-parameter tractable 

      Lokshtanov, Daniel; Saurabh, Saket; Sharma, Roohani; Zehavi, Meirav (Journal article; Peer reviewed, 2019)
      The family of judicious partitioning problems, introduced by Bollobás and Scott to the field of extremal combinatorics, has been extensively studied from a structural point of view for over two decades. This rich realm of ...
    • Connecting the Dots (with Minimum Crossings) 

      Agrawal, Akanksha; Guspiel, Grzegorz; Madathil, Jayakrishnan; Saurabh, Saket; Zehavi, Meirav (Journal article; Peer reviewed, 2019)
      We study a prototype Crossing Minimization problem, defined as follows. Let F be an infinite family of (possibly vertex-labeled) graphs. Then, given a set P of (possibly labeled) n points in the Euclidean plane, a collection ...
    • Connecting Vertices by Independent Trees 

      Basavaraju, Manu; Fomin, Fedor; Golovach, Petr; Saurabh, Saket (Conference object, 2014)
      We study the paramereteized complexity of the following connectivity problem. For a vertex subset U of a graph G, trees T1, . . . , Ts of G are completely independent spanning trees of U if each of them contains U , and ...
    • Covering Vectors by Spaces in Perturbed Graphic Matroids and Their Duals 

      Fomin, Fedor; Golovach, Petr; Lokshtanov, Daniel; Saurabh, Saket; Zehavi, Meirav (Peer reviewed; Journal article, 2019)
      Perturbed graphic matroids are binary matroids that can be obtained from a graphic matroid by adding a noise of small rank. More precisely, an r-rank perturbed graphic matroid M is a binary matroid that can be represented ...
    • Decomposition of map graphs with applications 

      Fomin, Fedor; Lokshtanov, Daniel; Panolan, Fahad; Saurabh, Saket; Zehavi, Meirav (Peer reviewed; Journal article, 2019)
    • Exact and approximate digraph bandwidth 

      Jain, Pallavi; Kanesh, Lawqueen; Lochet, William; Saurabh, Saket; Sharma, Roohani (Journal article; Peer reviewed, 2019)
      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 ...
    • Finding even subgraphs even faster 

      Goyal, Prachi; Misra, Pranabendu; Panolan, Fahad; Philip, Geevarghese; Saurabh, Saket (Conference object; Peer reviewed; Journal article, 2015)
      Problems of the following kind have been the focus of much recent research in the realm of parameterized complexity: Given an input graph (digraph) on n vertices and a positive integer parameter k, find if there exist k ...
    • Going Far From Degeneracy 

      Fomin, Fedor; Golovach, Petr; Lokshtanov, Daniel; Panolan, Fahad; Saurabh, Saket; Zehavi, Meirav (Peer reviewed; Journal article, 2019-09-06)
      An undirected graph G is d-degenerate if every subgraph of G has a vertex of degree at most d. By the classical theorem of Erd\H{o}s and Gallai from 1959, every graph of degeneracy d>1 contains a cycle of length at least ...
    • Kernel(s) for Problems with No Kernel: On Out-Trees with Many Leaves 

      Fernau, Henning; Fomin, Fedor; Lokshtanov, Daniel; Raible, Daniel; Saurabh, Saket; Villanger, Yngve (Conference object; Peer reviewed; Journal article, 2009)
      The {\sc \(k\)-Leaf Out-Branching} problem is to find an out-branching, that is a rooted oriented spanning tree, with at least \(k\) leaves in a given digraph. The problem has recently received much attention from the ...
    • On cutwidth parameterized by vertex cover 

      Cygan, Marek; Lokshtanov, Daniel; Pilipczuk, Marcin; Pilipczuk, Michal Pawel; Saurabh, Saket (Peer reviewed; Journal article, 2014-04)
      We study the CUTWIDTH problem, where the input is a graph G, and the objective is find a linear layout of the vertices that minimizes the maximum number of edges intersected by any vertical line inserted between two ...
    • Packing arc-disjoint cycles in tournaments 

      Bessy, Stephane; Bougeret, Marin; Krithika, R; Sahu, Abhishek; Saurabh, Saket; Thiebaut, Jocelyn; Zehavi, Meirav (Journal article; Peer reviewed, 2019)
      A tournament is a directed graph in which there is a single arc between every pair of distinct vertices. Given a tournament T on n vertices, we explore the classical and parameterized complexity of the problems of determining ...
    • Packing cycles faster than Erdos-Posa 

      Lokshtanov, Daniel; Mouawad, Amer E.; Saurabh, Saket; Zehavi, Meirav (Journal article; Peer reviewed, 2019)
      The Cycle Packing problem asks whether a given undirected graph $G=(V,E)$ contains $k$ vertex-disjoint cycles. Since the publication of the classic Erdös--Pósa theorem in 1965, this problem received significant attention ...
    • Parameterized complexity classification of deletion to list matrix-partition for low-order matrices 

      Agrawal, Akanksha; Kolay, Sudeshna; Madathil, Jayakrishnan; Saurabh, Saket (Journal article; Peer reviewed, 2019)
      Given a symmetric l x l matrix M=(m_{i,j}) with entries in {0,1,*}, a graph G and a function L : V(G) - > 2^{[l]} (where [l] = {1,2,...,l}), a list M-partition of G with respect to L is a partition of V(G) into l parts, ...
    • Parameterized complexity of conflict-free matchings and paths 

      Agrawal, Akanksha; Jain, Pallavi; Kanesh, Lawqueen; Saurabh, Saket (Journal article; Peer reviewed, 2019)
      An input to a conflict-free variant of a classical problem Gamma, called Conflict-Free Gamma, consists of an instance I of Gamma coupled with a graph H, called the conflict graph. A solution to Conflict-Free Gamma in (I,H) ...
    • Parameterized Single-Exponential Time Polynomial Space Algorithm for Steiner Tree 

      Fomin, Fedor; Kaski, Petteri; Lokshtanov, Daniel; Panolan, Fahad; Saurabh, Saket (Peer reviewed; Journal article, 2019)
      In the Steiner Tree problem, we are given as input a connected \(n\)-vertex graph with edge weights in \(\{1,2,\ldots,W\}\), and a set of \(k\) terminal vertices. Our task is to compute a minimum-weight tree that contains ...
    • Parameterized streaming algorithms for min-ones d-SAT 

      Agrawal, Akanksha; Bonnet, Édouard; Curticapean, Radu; Miltzow, Tillmann; Saurabh, Saket; Biswas, Arindam; Brettell, Nick; Marx, Dániel; Raman, Venkatesh (Journal article; Peer reviewed, 2019)
      In this work, we initiate the study of the Min-Ones d-SAT problem in the parameterized streaming model. An instance of the problem consists of a d-CNF formula F and an integer k, and the objective is to determine if F has ...
    • Path Contraction Faster Than 2n 

      Agrawal, Akanksha; Fomin, Fedor; Lokshtanov, Daniel; Saurabh, Saket; Tale, Prafullkumar (Peer reviewed; Journal article, 2019)
      A graph G is contractible to a graph H if there is a set X subseteq E(G), such that G/X is isomorphic to H. Here, G/X is the graph obtained from G by contracting all the edges in X. For a family of graphs F, the F-Contraction ...
    • Quick but odd growth of cacti 

      Kolay, Sudeshna; Lokshtanov, Daniel; Panolan, Fahad; Saurabh, Saket (Conference object; Peer reviewed; Journal article, 2015)
      Let F be a family of graphs. Given an input graph G and a positive integer k, testing whether G has a k-sized subset of vertices S, such that G\S belongs to F, is a prototype vertex deletion problem. These type of problems ...
    • Rank vertex cover as a natural problem for algebraic compression 

      Meesum, Syed Mohammad; Panolan, Fahad; Saurabh, Saket; Zehavi, Meirav (Journal article; Peer reviewed, 2019)
      The question of the existence of a polynomial kernelization of the Vertex Cover Above LP problem was a long-standing, notorious open problem in parameterized complexity. Some years ago, the breakthrough work by Kratsch and ...