Related papers: The Rectilinear Steiner Forest Arborescence proble…
Minimum $k$-Section denotes the NP-hard problem to partition the vertex set of a graph into $k$ sets of sizes as equal as possible while minimizing the cut width, which is the number of edges between these sets. When $k$ is an input…
We study the metric Steiner tree problem in the sublinear query model. In this problem, for a set of $n$ points $V$ in a metric space given to us by means of query access to an $n\times n$ matrix $w$, and a set of terminals $T\subseteq V$,…
A linear forest is a collection of vertex-disjoint paths. The Linear Arboricity Conjecture states that every graph of maximum degree $\Delta$ can be decomposed into at most $\lceil(\Delta+1)/2\rceil$ linear forests. We prove that $\Delta/2…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
The Radial Spanning Tree (RST) in dimension $d\geq2$ is a random geometric graph constructed on a homogeneous Poisson point process $\mathcal N$ in $\mathbb R^d$ augmented by the origin, with edges connecting each $x\in\mathcal N$ to the…
Given two rooted, ordered, and labeled trees $P$ and $T$ the tree inclusion problem is to determine if $P$ can be obtained from $T$ by deleting nodes in $T$. This problem has recently been recognized as an important query primitive in XML…
Finding a minimum spanning tree (MST) for $n$ points in an arbitrary metric space is a fundamental primitive for hierarchical clustering and many other ML tasks, but this takes $\Omega(n^2)$ time to even approximate. We introduce a…
Tree containment problem is a fundamental problem in phylogenetic study, as it is used to verify a network model. It asks whether a given network contain a subtree that resembles a binary tree. The problem is NP-complete in general, even in…
In this paper, we consider Steiner forest and its generalizations, prize-collecting Steiner forest and k-Steiner forest, when the vertices of the input graph are points in the Euclidean plane and the lengths are Euclidean distances. First,…
Given a set $P$ of $n$ red and blue points in the plane, a \emph{planar bichromatic spanning tree} of $P$ is a spanning tree of $P$, such that each edge connects between a red and a blue point, and no two edges intersect. In the bottleneck…
In the Directed Steiner Tree (DST) problem we are given an $n$-vertex directed edge-weighted graph, a root $r$, and a collection of $k$ terminal nodes. Our goal is to find a minimum-cost arborescence that contains a directed path from $r$…
In the Continuous Steiner Tree problem (CST), we are given as input a set of points (called terminals) in a metric space and ask for the minimum-cost tree connecting them. Additional points (called Steiner points) from the metric space can…
In this paper, we introduce a polynomial-time 2-approximation algorithm for the Unrooted Prize-Collecting Forest with $K$ Components (URPCF$_K$) problem. URPCF$_K$ aims to find a forest with exactly $K$ connected components while minimizing…
r-gathering problem is a variant of facility location problems. In this problem, we are given a set of users and a set of facilities on same metric space. We open some of the facilities and assign each user to an open facility, so that at…
We consider connectivity problems with orientation constraints. Given a directed graph $D$ and a collection of ordered node pairs $P$ let $P[D]=\{(u,v) \in P: D {contains a} uv{-path}}$. In the {\sf Steiner Forest Orientation} problem we…
Recently the authors [CCLMST23] introduced the notion of shortcut partition of planar graphs and obtained several results from the partition, including a tree cover with $O(1)$ trees for planar metrics and an additive embedding into small…
The maximum agreement forest (MAF) problem in phylogenetics takes as input a set t >= 2 of binary phylogenetic trees T on the same set of taxa X. It asks for a partition of X into the smallest number of blocks such that the subtrees induced…
The \emph{Steiner tree} problem is one of the fundamental and classical problems in combinatorial optimization. In this paper, we study this problem in the $\mathcal{CONGESTED}$ $\mathcal{CLIQUE}$ model of distributed computing and present…
We study the following two maximization problems related to spanning trees in the Euclidean plane. It is not known whether or not these problems are NP-hard. We present approximation algorithms with better approximation ratios for both…
We consider a general metric Steiner problem which is of finding a set $\mathcal{S}$ with minimal length such that $\mathcal{S} \cup A$ is connected, where $A$ is a given compact subset of a given complete metric space $X$; a solution is…