Browsing Department of Informatics by Author "Fomin, Fedor"
Now showing items 21-40 of 62
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FPT Approximation for Fair Minimum-Load Clustering
Bandyapadhyay, Sayan; Fomin, Fedor; Golovach, Petr; Purohit, Nidhi; Simonov, Kirill (Journal article; Peer reviewed, 2022)In this paper, we consider the Minimum-Load k-Clustering/Facility Location (MLkC) problem where we are given a set P of n points in a metric space that we have to cluster and an integer k > 0 that denotes the number of ... -
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, 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 ... -
How to find a good explanation for clustering?
Bandyapadhyay, Sayan; Fomin, Fedor; Golovach, Petr; Lochet, William Alexandre; Purohit, Nidhi; Simonov, Kirill (Journal article; Peer reviewed, 2023)k-means and k-median clustering are powerful unsupervised machine learning techniques. However, due to complicated dependencies on all the features, it is challenging to interpret the resulting cluster assignments. Moshkovitz, ... -
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 (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 ... -
Kernelization of Graph Hamiltonicity: Proper H-Graphs
Chaplick, Steven; Fomin, Fedor; Golovach, Petr; Knop, Dusan; Zeman, Peter (Journal article; Peer reviewed, 2021)We obtain new polynomial kernels and compression algorithms for Path Cover and Cycle Cover, the well-known generalizations of the classical Hamiltonian Path and Hamiltonian Cycle problems. Our choice of parameterization ... -
Kernelization of Whitney Switches
Fomin, Fedor; Golovach, Petr (Journal article; Peer reviewed, 2020)A fundamental theorem of Whitney from 1933 asserts that 2-connected graphs G and H are 2-isomorphic, or equivalently, their cycle matroids are isomorphic, if and only if G can be transformed into H by a series of operations ... -
Kernelization of Whitney Switches
Fomin, Fedor; Golovach, Petr (Journal article; Peer reviewed, 2021)A fundamental theorem of Whitney from 1933 asserts that 2-connected graphs $G$ and $H$ are 2-isomorphic, or equivalently, their cycle matroids are isomorphic if and only if $G$ can be transformed into $H$ by a series of ... -
Largest chordal and interval subgraphs faster than 2n
Bliznets, Ivan; Fomin, Fedor; Pilipczuk, Michal Pawel; Villanger, Yngve (Peer reviewed; Journal article, 2015-08-22)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) ... -
Long Cycles in Graphs: Extremal Combinatorics Meets Parameterized Algorithms
Fomin, Fedor; Golovach, Petr; Sagunov, Danil; Simonov, Kirill (Journal article; Peer reviewed, 2022)We discuss recent algorithmic extensions of two classic results of extremal combinatorics about long paths in graphs. First, the theorem of Dirac from 1952 asserts that a 2-connected graph G with the minimum vertex degree ... -
Longest Cycle Above Erdös-Gallai Bound
Fomin, Fedor; Golovach, Petr; Sagunov, Danil; Simonov, Kirill (Journal article; Peer reviewed, 2022)In 1959, Erdős and Gallai proved that every graph G with average vertex degree ad(G) ≥ 2 contains a cycle of length at least ad(G). We provide an algorithm that for k ≥ 0 in time 2^𝒪(k)⋅n^𝒪(1) decides whether a 2-connected ... -
Lossy Kernelization of Same-Size Clustering
Bandyapadhyay, Sayan; Fomin, Fedor; Golovach, Petr; Purohit, Nidhi; Simonov, Kirill (Journal article; Peer reviewed, 2023)In this work, we study the k-median clustering problem with an additional equal-size constraint on the clusters from the perspective of parameterized preprocessing. Our main result is the first lossy (2-approximate) ... -
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 ... -
Minimum Fill-in of Sparse Graphs: Kernelization and Approximation
Fomin, Fedor; Geevarghese, Philip; Villanger, Yngve (Peer reviewed; Journal article, 2011)The Minimum Fill-in 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 k-vertex labeled graph to another k-vertex graph. We consider a general family of graph modification problems, called L-Replacement 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, 2011-01-21)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 ... -
On the Complexity of Recovering Incidence Matrices
Fomin, Fedor; Golovach, Petr; Misra, Pranabendu; Ramanujan, M.S. (Journal article; Peer reviewed, 2020)The incidence matrix of a graph is a fundamental object naturally appearing in many applications, involving graphs such as social networks, communication networks, or transportation networks. Often, the data collected about ... -
On the Parameterized Complexity of the Expected Coverage Problem
Fomin, Fedor; Ramamoorthi, Vijayaragunathan (Journal article; Peer reviewed, 2022)The MAXIMUM COVERING LOCATION PROBLEM (MCLP) is a well-studied problem in the field of operations research. Given a network with positive or negative demands on the nodes, a positive integer k, the MCLP seeks to find k ... -
On the Tractability of Optimization Problems on H-Graphs
Fomin, Fedor; Golovach, Petr; Raymond, Jean-Florent (Journal article; Peer reviewed, 2020)For a graph H, a graph G is an H-graph if it is an intersection graph of connected subgraphs of some subdivision of H. H-graphs naturally generalize several important graph classes like interval graphs or circular-arc ... -
On width measures and topological problems on semi-complete digraphs
Fomin, Fedor; Pilipczuk, Michal (Peer reviewed; Journal article, 2019)The topological theory for semi-complete digraphs, pioneered by Chudnovsky, Fradkin, Kim, Scott, and Seymour [10], [11], [12], [28], [43], [39], concentrates on the interplay between the most important width measures — ...