Browsing Bergen Open Research Archive by Author "Fomin, Fedor"
Now showing items 120 of 36

An Algorithmic MetaTheorem for Graph Modification to Planarity and FOL
Fomin, Fedor; Golovach, Petr; Stamoulis, Giannos; Thilikos, Dimitrios M. (Journal article; Peer reviewed, 2020)In general, a graph modification problem is defined by a graph modification operation ⊠ and a target graph property 𝒫. Typically, the modification operation ⊠ may be vertex removal, edge removal, edge contraction, or edge ... 
Approximating Acyclicity Parameters of Sparse Hypergraphs
Fomin, Fedor; Golovach, Petr; Thilikos, Dimitrios (Conference object; Peer reviewed; Journal article, 2009)The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello (PODS'99, PODS'01) in order to extend the concept of hypergraph acyclicity. These notions were further generalized ... 
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, ... 
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 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) 
Diverse Pairs of Matchings
Fomin, Fedor; Golovach, Petr; Jaffke, Lars; Philip, Geevarghese; Sagunov, Danil (Journal article; Peer reviewed, 2020)We initiate the study of the Diverse Pair of (Maximum/ Perfect) Matchings problems which given a graph G and an integer k, ask whether G has two (maximum/perfect) matchings whose symmetric difference is at least k. Diverse ... 
Exact algorithms for treewidth and minimum fillin
Fomin, Fedor; Todinca, Ioan; Kratsch, Dieter; Villanger, Yngve (Journal article, 2006) 
Exploring Subexponential Parameterized Complexity of Completion Problems
Drange, Pål Grønås; Fomin, Fedor; Pilipczuk, Michal Pawel; Villanger, Yngve (Peer reviewed; Journal article, 20140219)Let F be a family of graphs. In the FCompletion problem, we are given an nvertex graph G and an integer k as input, and asked whether at most k edges can be added to G so that the resulting graph does not contain a graph ... 
Finding Induced Subgraphs via Minimal Triangulations
Fomin, Fedor; Villanger, Yngve (Conference object; Peer reviewed; Journal article, 2010)Potential maximal cliques and minimal separators are combinatorial objects which were introduced and studied in the realm of minimal triangulation problems in cluding Minimum Fillin and Treewidth. We discover unexpected ... 
A FixedParameter Perspective on #BIS
Curticapean, Radu; Dell, Holger; Fomin, Fedor; Goldberg, Leslie Ann; Lapinskas, John (Peer reviewed; Journal article, 20190718)The problem of (approximately) counting the independent sets of a bipartite graph (#BIS) is the canonical approximate counting problem that is complete in the intermediate complexity class #RHΠ1. It is believed that #BIS ... 
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 ... 
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 ... 
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 ... 
Kernelization of Whitney Switches
Fomin, Fedor; Golovach, Petr (Journal article; Peer reviewed, 2020)A fundamental theorem of Whitney from 1933 asserts that 2connected graphs G and H are 2isomorphic, or equivalently, their cycle matroids are isomorphic, if and only if G can be transformed into H by a series of operations ... 
Largest chordal and interval subgraphs faster than 2n
Bliznets, Ivan; Fomin, Fedor; Pilipczuk, Michal Pawel; Villanger, Yngve (Peer reviewed; Journal article, 20150822)We prove that in a graph with n vertices, induced chordal and interval subgraphs with the maximum number of vertices can be found in time O(2λn) for some λ< 1. These are the first algorithms breaking the trivial 2nnO(1) ... 
LowRank Binary Matrix Approximation in ColumnSum Norm
Fomin, Fedor; Golovach, Petr; Panolan, Fahad; Simonov, Kirill (Journal article; Peer reviewed, 2020)We consider 𝓁₁Rankr 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 columnsum norm ‖ 𝐀 𝐁‖₁. We show ... 
Minimum Fillin of Sparse Graphs: Kernelization and Approximation
Fomin, Fedor; Geevarghese, Philip; Villanger, Yngve (Conference object; Peer reviewed; Journal article, 2011)The Minimum Fillin problem is to decide if a graph can be triangulated by adding at most k edges. The problem has important applications in numerical algebra, in particular in sparse matrix computations. We develop ... 
Modification to planarity is fixed parameter tractable
Fomin, Fedor; Golovach, Petr; Thilikos, Dimitrios M (Peer reviewed; Journal article, 2019)A replacement action is a function L that maps each kvertex labeled graph to another kvertex graph. We consider a general family of graph modification problems, called LReplacement to C, where the input is a graph G and ... 
A Note on Exact Algorithms for Vertex Ordering Problems on Graphs
Bodlaender, Hans L.; Fomin, Fedor; Koster, Arie M.C.A.; Kratsch, Dieter; Thilikos, Dimitrios M. (Peer reviewed; Journal article, 20110121)In this note, we give a proof that several vertex ordering problems can be solved in O ∗(2 n ) time and O ∗(2 n ) space, or in O ∗(4 n ) time and polynomial space. The algorithms generalize algorithms for the Travelling ...