Related papers: Induced Subforests and Superforests
We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small tree-width, and applying dynamic…
We propose the first branch-&-price algorithm for the maximum agreement forest problem on unrooted binary trees: given two unrooted X-labelled binary trees we seek to partition X into a minimum number of blocks such that the induced…
We address here spanning tree problems on a graph with binary edge weights. For a general weighted graph the minimum spanning tree is solved in super-linear running time, even when the edges of the graph are pre-sorted. A related problem,…
Deciding whether a graph can be edge-decomposed into a matching and a $k$-bounded linear forest was recently shown by Campbell, H{\"o}rsch and Moore to be NP-complete for every $k \ge 9$, and solvable in polynomial time for $k=1,2$. In the…
We study the densest subgraph problem and its NP-hard densest at-most-$k$ subgraph variant through the lens of learning-augmented algorithms. We show that, given a reasonably accurate predictor that estimates whether a node belongs to the…
Many popular algorithms for searching the space of leaf-labelled trees are based on tree rearrangement operations. Under any such operation, the problem is reduced to searching a graph where vertices are trees and (undirected) edges are…
For a metric graph $G=(V,E)$ and $R\subset V$, the internal Steiner minimum tree problem asks for a minimum weight Steiner tree spanning $R$ such that every vertex in $R$ is not a leaf. This note shows a simple polynomial-time…
A double-arborescence is a treelike comparability graph with an all-adjacent vertex. In this paper, we first give a forbidden induced subgraph characterization of double-arborescences, where we prove that double-arborescences are precisely…
In this article, we construct explicit examples of pairs of non-isomorphic trees with the same restricted $U$-polynomial for every $k$; by this we mean that the polynomials agree on terms with degree at most $k+1$. The main tool for this…
Probabilistic inferences distill knowledge from graphs to aid human make important decisions. Due to the inherent uncertainty in the model and the complexity of the knowledge, it is desirable to help the end-users understand the inference…
We study the problem of constructing universal Steiner trees for undirected graphs. Given a graph $G$ and a root node $r$, we seek a single spanning tree $T$ of minimum {\em stretch}, where the stretch of $T$ is defined to be the maximum…
Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views,…
We give approximation schemes for Subset TSP and Steiner Tree on unit disk graphs, and more generally, on intersection graphs of similarly sized connected fat (not necessarily convex) polygons in the plane. As a first step towards this…
In this paper, we study the complexity of the periodic temporal graph realization problem with respect to upper bounds on the fastest path durations among its vertices. This constraint with respect to upper bounds appears naturally in…
In the spanning tree congestion problem, given a connected graph $G$, the objective is to compute a spanning tree $T$ in $G$ that minimizes its maximum edge congestion, where the congestion of an edge $e$ of $T$ is the number of edges in…
We consider the $k$-prize-collecting Steiner tree problem. An instance is composed of an integer $k$ and a graph $G$ with costs on edges and penalties on vertices. The objective is to find a tree spanning at least $k$ vertices which…
In a classical covering problem, we are given a set of requests that we need to satisfy (fully or partially), by buying a subset of items at minimum cost. For example, in the k-MST problem we want to find the cheapest tree spanning at least…
Let $H$ be a fixed graph. The $H$-Transversal problem, given a graph $G$, asks to remove the smallest number of vertices from $G$ so that $G$ does not contain $H$ as a subgraph. While a simple $|V(H)|$-approximation algorithm exists and is…
A widely studied problem in communication networks is that of finding the maximum number of communication requests that can be scheduled concurrently, subject to node and/or link capacity constraints. In this paper, we consider the problem…
We present a series of almost settled inapproximability results for three fundamental problems. The first in our series is the subexponential-time inapproximability of the maximum independent set problem, a question studied in the area of…