• A (2 + ε)-Factor Approximation Algorithm for Split Vertex Deletion 

      Lokshtanov, Daniel; Misra, Pranabendu; Panolan, Fahad; Philip, Geevarghese; Saurabh, Saket (Journal article; Peer reviewed, 2020)
      In the Split Vertex Deletion (SVD) problem, the input is an n-vertex undirected graph G and a weight function w: V(G) → ℕ, and the objective is to find a minimum weight subset S of vertices such that G-S is a split graph ...
    • Complexity of the Steiner Network Problem with Respect to the Number of Terminals 

      Eiben, Eduard; Knop, Dusan; Panolan, Fahad; Suchý, Ondřej (Journal article; Peer reviewed, 2019)
      In the Directed Steiner Network problem we are given an arc-weighted digraph G, a set of terminals T subseteq V(G) with |T|=q, and an (unweighted) directed request graph R with V(R)=T. Our task is to output a subgraph H ...
    • Diverse Collections in Matroids and Graphs 

      Fomin, Fedor; Golovach, Petr; Panolan, Fahad; Philip, Geevarghese; Saurabh, Saket (Journal article; Peer reviewed, 2021)
      We investigate the parameterized complexity of finding diverse sets of solutions to three fundamental combinatorial problems, two from the theory of matroids and the third from graph theory. The input to the Weighted Diverse ...
    • ETH-tight algorithms for long path and cycle on unit disk graphs 

      Fomin, Fedor; Lokshtanov, Daniel; Panolan, Fahad; Saurabh, Saket; Zehavi, Meirav (Journal article; Peer reviewed, 2020)
      We present an algorithm for the extensively studied Long Path and Long Cycle problems on unit disk graphs that runs in time 2O(√k)(n + m). Under the Exponential Time Hypothesis, Long Path and Long Cycle on unit disk graphs ...
    • Going Far from Degeneracy 

      Fomin, Fedor; Golovach, Petr; Lokshtanov, Daniel; Panolan, Fahad; Saurabh, Saket; Zehavi, Meirav (Journal article; Peer reviewed, 2020)
      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 Erdös and Gallai from 1959, every graph of degeneracy $d>1$ contains a cycle of length at ...
    • Low-Rank Binary Matrix Approximation in Column-Sum Norm 

      Fomin, Fedor; Golovach, Petr; Panolan, Fahad; Simonov, Kirill (Journal article; Peer reviewed, 2020)
      We consider 𝓁₁-Rank-r Approximation over {GF}(2), where for a binary m× n matrix 𝐀 and a positive integer constant r, one seeks a binary matrix 𝐁 of rank at most r, minimizing the column-sum norm ‖ 𝐀 -𝐁‖₁. We show ...
    • Parameterization Above a Multiplicative Guarantee 

      Fomin, Fedor; Golovach, Petr; Lokshtanov, Daniel; Panolan, Fahad; Saurabh, Saket; Zehavi, Meirav (Journal article; Peer reviewed, 2020)
      Parameterization above a guarantee is a successful paradigm in Parameterized Complexity. To the best of our knowledge, all fixed-parameter tractable problems in this paradigm share an additive form defined as follows. Given ...
    • Quick separation in chordal and split graphs 

      Misra, Pranabendu; Panolan, Fahad; Rai, Ashutosh; Saurabh, Saket; Sharma, Roohani (Journal article; Peer reviewed, 2020)
      In this paper we study two classical cut problems, namely Multicut and Multiway Cut on chordal graphs and split graphs. In the Multicut problem, the input is a graph G, a collection of 𝓁 vertex pairs (si, ti), i ∈ [𝓁], ...
    • 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 ...