Browsing Bergen Open Research Archive by Author "Lokshtanov, Daniel"
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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 nvertex 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 GS is a split graph ... 
bColoring Parameterized by CliqueWidth
Jaffke, Lars; Lima, Paloma Thome de; Lokshtanov, Daniel (Journal article; Peer reviewed, 2021)We provide a polynomialtime algorithm for bColoring on graphs of constant cliquewidth. This unifies and extends nearly all previously known polynomialtime results on graph classes, and answers open questions posed by ... 
Balanced judicious bipartition is fixedparameter 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 ... 
Bidimensionality and Kernels
Fomin, Fedor; Lokshtanov, Daniel; Saurabh, Saket; Thilikos, Dimitrios (Journal article; Peer reviewed, 2020)Bidimensionality theory was introduced by [E. D. Demaine et al., J. ACM, 52 (2005), pp. 866893] as a tool to obtain subexponential time parameterized algorithms on Hminorfree graphs. In [E. D. Demaine and M. Hajiaghayi, ... 
Bisection of Bounded Treewidth Graphs by Convolutions
Eiben, Eduard; Lokshtanov, Daniel; Mouawad, Amer E. (Journal article; Peer reviewed, 2019)In the Bisection problem, we are given as input an edgeweighted graph G. The task is to find a partition of V(G) into two parts A and B such that A  B <= 1 and the sum of the weights of the edges with one endpoint ... 
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 rrank 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) 
ETHtight 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 ... 
Fault tolerant subgraphs with applications in kernelization
Lochet, William; Lokshtanov, Daniel; Misra, Pranabendu; Saurabh, Saket; Sharma, Roohani; Zehavi, Meirav (Journal article; Peer reviewed, 2020)In the past decade, the design of fault tolerant data structures for networks has become a central topic of research. Particular attention has been given to the construction of a subgraph H of a given digraph D with as ... 
Fixed Parameter Set Splitting, Linear Kernel and Improved Running Time
Lokshtanov, Daniel; Sloper, Christian (2005) 
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 ... 
Going Far From Degeneracy
Fomin, Fedor; Golovach, Petr; Lokshtanov, Daniel; Panolan, Fahad; Saurabh, Saket; Zehavi, Meirav (Peer reviewed; Journal article, 20190906)An undirected graph G is ddegenerate 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 OutTrees 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 OutBranching} problem is to find an outbranching, 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, 201404)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 cycles faster than ErdosPosa
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 $k$ vertexdisjoint cycles. Since the publication of the classic ErdösPósa theorem in 1965, this problem received significant attention ... 
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 fixedparameter tractable problems in this paradigm share an additive form defined as follows. Given ... 
The Parameterized Complexity of Guarding Almost Convex Polygons
Agrawal, Akanksha; Knudsen, Kristine Vitting Klinkby; Lokshtanov, Daniel; Saurabh, Saket; Zehavi, Meirav (Journal article; Peer reviewed, 2020)The Art Gallery problem is a fundamental visibility problem in Computational Geometry. The input consists of a simple polygon P, (possibly infinite) sets G and C of points within P, and an integer k; the task is to decide ... 
Parameterized SingleExponential 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 minimumweight tree that contains ... 
Path contraction faster than $2^n$
Agrawal, Akanksha; Fomin, Fedor; Lokshtanov, Daniel; Saurabh, Saket; Tale, Prafullkumar (Journal article; Peer reviewed, 2020)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 ... 
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 FContraction ...