Iskanje po repozitoriju

Computing tree decompositions with small independence number
Clément Jean Dallard, Fedor V. Fomin, Petr A. Golovach, Tuukka Korhonen, Martin Milanič, 2026, izvirni znanstveni članek

Opis: The independence number of a tree decomposition is the maximum of the independence numbers of the subgraphs induced by its bags. The tree-independence number of a graph is the minimum independence number of a tree decomposition of it. Several NP-hard graph problems, like maximum-weight independent set, can be solved in time n^O(k) if the input n-vertex graph is given together with a tree decomposition of independence number k. Yolov, in SODA 2018, gave an algorithm that, given an n-vertex graph G and an integer k, in time n^O(k^3) either constructs a tree decomposition of G whose independence number is O(k^3) or correctly reports that the tree-independence number of G is larger than k. In this article, we first give an algorithm for computing the tree-independence number with a better approximation ratio and running time and then prove that our algorithm is, in some sense, the best one can hope for. Our second result is that the exact computation of the tree-independence number is para-NP-hard: We show that for every constant k ≥ 4 it is NP-complete to decide whether a given graph has the tree-independence number at most k.
Ključne besede: tree-independence number, approximation, parameterized algorithm
Objavljeno v RUP: 16.12.2025; Ogledov: 238; Prenosov: 3
Celotno besedilo (1,45 MB)
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Perfect phylogenies via branchings in acyclic digraphs and a generalization of Dilworth's theorem
Ademir Hujdurović, Martin Milanič, Edin Husić, Romeo Rizzi, Alexandru I. Tomescu, 2017, objavljeni povzetek znanstvenega prispevka na konferenci

Ključne besede: perfect phylogeny, NP-hard problem, branching, acyclic digraph, chain partition, Dilworth's theorem, min-max theorem, approximation algorithm, heuristic
Objavljeno v RUP: 17.09.2018; Ogledov: 3827; Prenosov: 125
Povezava na celotno besedilo

Reconstructing perfect phylogenies via binary matrices, branchings in DAGs, and a generalization of Dilworth's theorem
Martin Milanič, 2018, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Ključne besede: perfect phylogeny, NP-hard problem, graph coloring, branching, acyclic digraph, chain partition, Dilworth's theorem, min-max theorem, approximation algorithm, heuristic
Objavljeno v RUP: 17.09.2018; Ogledov: 3428; Prenosov: 22
Povezava na celotno besedilo

The minimum conflict-free row split problem revisited
Ademir Hujdurović, Edin Husić, Martin Milanič, Romeo Rizzi, Alexandru I. Tomescu, 2016, objavljeni znanstveni prispevek na konferenci

Ključne besede: #the #minimum conflict-free row split problem, branching, Dilworth's theorem, min-max theorem, approximation algorithm, APX-hardness
Objavljeno v RUP: 14.11.2017; Ogledov: 5075; Prenosov: 287
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