Related papers: Algorithms for Cut Problems on Trees

Unbreakable decomposition, introduced by Cygan et al. (SICOMP'19) and Cygan et al. (TALG'20), has proven to be one of the most powerful tools for parameterized graph cut problems in recent years. Unfortunately, all known constructions…

In the k-Path problem, the input is a directed graph $G$ and an integer $k\geq 1$, and the goal is to decide whether there is a simple directed path in $G$ with exactly $k$ vertices. We give a deterministic algorithm for k-Path with time…

We study the shared processor scheduling problem with a single shared processor where a unit time saving (weight) obtained by processing a job on the shared processor depends on the job. A polynomial-time optimization algorithm has been…

We consider the problems ZERO EXTENSION and METRIC LABELLING under the paradigm of parameterized complexity. These are natural, well-studied problems with important applications, but have previously not received much attention from…

We study the problem of multiway number partition optimization, which has a myriad of applications in the decision, learning and optimization literature. Even though the original multiway partitioning problem is NP-hard and requires…

We investigate the parameterized complexity of the Isometric Path Partition problem when parameterized by the treewidth ($\mathrm{tw}$) of the input graph, arguably one of the most widely studied parameters. Courcelle's theorem shows that…

We show the existence of an exact mimicking network of $k^{O(\log k)}$ edges for minimum multicuts over a set of terminals in an undirected graph, where $k$ is the total capacity of the terminals, as well as a method for computing a…

In parameterized complexity, it is a natural idea to consider different generalizations of classic problems. Usually, such generalization are obtained by introducing a "relaxation" variable, where the original problem corresponds to setting…

We present approximation algorithms for the following NP-hard optimization problems related to bottleneck spanning trees in metric spaces. 1. The disjoint bottleneck spanning tree problem: Given $n$ pairs of points in a metric space, find…

We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…

One way to state the Load Coloring Problem (LCP) is as follows. Let $G=(V,E)$ be graph and let $f:V\rightarrow \{{\rm red}, {\rm blue}\}$ be a 2-coloring. An edge $e\in E$ is called red (blue) if both end-vertices of $e$ are red (blue). For…

We study a broad class of graph partitioning problems, where each problem is specified by a graph $G=(V,E)$, and parameters $k$ and $p$. We seek a subset $U\subseteq V$ of size $k$, such that $\alpha_1m_1 + \alpha_2m_2$ is at most (or at…

We introduce a new technique for designing fixed-parameter algorithms for cut problems, namely randomized contractions. We apply our framework to obtain the first FPT algorithm for the Unique Label Cover problem and new FPT algorithms with…

We consider the {\em Shaped Partition Problem} of partitioning $n$ given vectors in real $k$-space into $p$ parts so as to maximize an arbitrary objective function which is convex on the sum of vectors in each part, subject to arbitrary…

The Subgraph Isomorphism problem is of considerable importance in computer science. We examine the problem when the pattern graph H is of bounded treewidth, as occurs in a variety of applications. This problem has a well-known algorithm via…

We consider problems in which we are given a rooted tree as input, and must find a subtree with the same root, optimizing some objective function of the nodes in the subtree. When this function is the sum of constant node weights, the…

An L(2,1)-labeling of a graph $G$ is an assignment $f$ from the vertex set $V(G)$ to the set of nonnegative integers such that $|f(x)-f(y)|\ge 2$ if $x$ and $y$ are adjacent and $|f(x)-f(y)|\ge 1$ if $x$ and $y$ are at distance 2, for all…

We propose a fixed-parameter tractable algorithm for the \textsc{Max-Cut} problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane with…

We present a randomized $O(m \log^2 n)$ work, $O(\text{polylog } n)$ depth parallel algorithm for minimum cut. This algorithm matches the work bounds of a recent sequential algorithm by Gawrychowski, Mozes, and Weimann [ICALP'20], and…

We consider the indirect covering subtree problem (Kim et al., 1996). The input is an edge weighted tree graph along with customers located at the nodes. Each customer is associated with a radius and a penalty. The goal is to locate a…