Related papers: On Minimal Tree Realizations of Linear Codes
Minimal spanning trees on infinite vertex sets are investigated. A criterion for minimality of a spanning tree having a finite length is obtained, which generalizes the corresponding classical result for finite sets. It is given an analytic…
Given a graph $G=(V,E)$, the minimum branch vertices problem consists in finding a spanning tree $T=(V,E')$ of $G$ minimizing the number of vertices with degree greater than two. We consider a simple combinatorial lower bound for the…
A resolving set $S$ of a graph $G$ is a subset of its vertices such that no two vertices of $G$ have the same distance vector to $S$. The Metric Dimension problem asks for a resolving set of minimum size, and in its decision form, a…
The twin-width of a graph measures its distance to co-graphs and generalizes classical width concepts such as tree-width or rank-width. Since its introduction in 2020 (Bonnet et. al. 2020), a mass of new results has appeared relating twin…
A construction is presented that allows to produce subspace codes of long length using subspace codes of shorter length in combination with a rank metric code. The subspace distance of the resulting code, called linkage code, is as good as…
Tree-width and path-width are widely successful concepts. Many NP-hard problems have efficient solutions when restricted to graphs of bounded tree-width. Many efficient algorithms are based on a tree decomposition. Sometimes the more…
Linear constraints for a matrix polytope with no fractional vertex are investigated as intersecting research among permutation codes, rank modulations, and linear programming methods. By focusing the discussion to the block structure of…
We present a novel algorithm for the minimum-depth elimination tree problem, which is equivalent to the optimal treedepth decomposition problem. Our algorithm makes use of two cheaply-computed lower bound functions to prune the search tree,…
In 2019, Dvo\v{r}\'{a}k asked whether every connected graph $G$ has a tree decomposition $(T, \mathcal{B})$ so that $T$ is a subgraph of $G$ and the width of $(T, \mathcal{B})$ is bounded by a function of the treewidth of $G$. We prove that…
A phylogenetic tree shows the evolutionary relationships among species. Internal nodes of the tree represent speciation events and leaf nodes correspond to species. A goal of phylogenetics is to combine such trees into larger trees, called…
Hypertree decompositions of hypergraphs are a generalization of tree decompositions of graphs. The corresponding hypertree-width is a measure for the cyclicity and therefore tractability of the encoded computation problem. Many NP-hard…
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…
A complexity-adaptive tree search algorithm is proposed for $\boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding by using a successive decoding schedule. The average complexity is close to that of the successive…
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.…
Computing bounded depth decompositions is a bottleneck in many applications of the treedepth parameter. The fastest known algorithm, which is due to Reidl, Rossmanith, S\'{a}nchez Villaamil, and Sikdar [ICALP 2014], runs in…
In this work we show how to decompose a linear code relatively to any given poset metric. We prove that the complexity of syndrome decoding is determined by a maximal (primary) such decomposition and then show that a refinement of a partial…
Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, such dynamic programming…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
In this article we study the treewidth of the \emph{display graph}, an auxiliary graph structure obtained from the fusion of phylogenetic (i.e., evolutionary) trees at their leaves. Earlier work has shown that the treewidth of the display…