Related papers: Light Spanner and Monotone Tree

Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…

The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to…

The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the graph parameter treewidth plays with respect to minors. In this paper, we provide the first algorithmic applications of tree-cut…

In the PATH COVER problem, one asks to cover the vertices of a graph using the smallest possible number of (not necessarily disjoint) paths. While the variant where the paths need to be pairwise vertex-disjoint, which we call PATH…

Span program is a linear-algebraic model of computation originally proposed for studying the complexity theory. Recently, it has become a useful tool for designing quantum algorithms. In this paper, we present a time-efficient…

Graph sketching is a powerful paradigm for analyzing graph structure via linear measurements introduced by Ahn, Guha, and McGregor (SODA'12) that has since found numerous applications in streaming, distributed computing, and massively…

We study multi-marginal optimal transport (MOT) problems where the underlying cost has a graphical structure. These graphical multi-marginal optimal transport problems have found applications in several domains including traffic flow…

Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised…

We develop fast approximation algorithms for the minimum-cost version of the Bounded-Degree MST problem (BD-MST) and its generalization the Crossing Spanning Tree problem (Crossing-ST). We solve the underlying LP to within a $(1+\epsilon)$…

Learning-based planners leveraging Graph Neural Networks can learn search guidance applicable to large search spaces, yet their potential to address symmetries remains largely unexplored. In this paper, we introduce a graph representation…

We consider the problem of uniformly generating a spanning tree, of a connected undirected graph. This process is useful to compute statistics, namely for phylogenetic trees. We describe a Markov chain for producing these trees. For cycle…

We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…

The Stacker Crane Problem (SCP) is a variant of the Traveling Salesman Problem. In SCP, pairs of pickup and delivery points are designated on a graph, and a crane must visit these points to move objects from each pickup location to its…

We investigate the problem of sequentially predicting the binary labels on the nodes of an arbitrary weighted graph. We show that, under a suitable parametrization of the problem, the optimal number of prediction mistakes can be…

Treewidth is a well-known graph invariant with multiple interesting applications in combinatorics. On the practical side, many NP-complete problems are polynomial-time (sometimes even linear-time) solvable on graphs of bounded treewidth. On…

Several novel mixed-integer linear and bilinear formulations are proposed for the optimum communication spanning tree problem. They implement the distance-based approach: graph distances are directly modeled by continuous, integral, or…

For many problems, the important instances from practice possess certain structure that one should reflect in the design of specific algorithms. As data reduction is an important and inextricable part of today's computation, we employ one…

We present the first polynomial-time approximation schemes, i.e., (1 + {\epsilon})-approximation algorithm for any constant {\epsilon} > 0, for the minimum three-edge connected spanning subgraph problem and the minimum three-vertex…

In this paper, we investigate the $k$-path coloring problem, a variant of vertex coloring arising in the context of integrated circuit manufacturing. In this setting, typical industrial instances exhibit a `tree-like' structure. We exploit…

Suffix trees are an important data structure at the core of optimal solutions to many fundamental string problems, such as exact pattern matching, longest common substring, matching statistics, and longest repeated substring. Recent lines…