相关论文: Bidimensionality and EPTAS

Retraction note: After posting the manuscript on arXiv, we were informed by Erik Jan van Leeuwen that both results were known and they appeared in his thesis[vL09]. A PTAS for MDS is at Theorem 6.3.21 on page 79 and A PTAS for MCDS is at…

The notion of directed treewidth was introduced by Johnson, Robertson, Seymour and Thomas [Journal of Combinatorial Theory, Series B, Vol 82, 2001] as a first step towards an algorithmic metatheory for digraphs. They showed that some…

We study classic scheduling problems on uniformly related machines. Efficient polynomial time approximation schemes (EPTAS's) are fast and practical approximation schemes. New methods and techniques are essential in developing such improved…

In this paper we revisit the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal…

We introduce and study the complexity of Path Packing. Given a graph $G$ and a list of paths, the task is to embed the paths edge-disjoint in $G$. This generalizes the well known Hamiltonian-Path problem. Since Hamiltonian Path is…

For numerous graph problems in the realm of parameterized algorithms, using the size of a smallest deletion set (called a modulator) into well-understood graph families as parameterization has led to a long and successful line of research.…

In the Triangle-Free (Simple) 2-Matching problem we are given an undirected graph $G=(V,E)$. Our goal is to compute a maximum-cardinality $M\subseteq E$ satisfying the following properties: (1) at most two edges of $M$ are incident on each…

We develop a new approach for distributed distance computation in planar graphs that is based on a variant of the metric compression problem recently introduced by Abboud et al. [SODA'18]. One of our key technical contributions is in…

In their seminal work, Mustafa and Ray (2009) showed that a wide class of geometric set cover (SC) problems admit a PTAS via local search -- this is one of the most general approaches known for such problems. Their result applies if a…

We show that a simple local search gives a PTAS for the Feedback Vertex Set (FVS) problem in minor-free graphs. An efficient PTAS in minor-free graphs was known for this problem by Fomin, Lokshtanov, Raman and Sauraubh. However, their…

In this paper we study a scheduling problem arising from executing numerical simulations on HPC architectures. With a constant number of parallel machines, the objective is to minimize the makespan under memory constraints for the machines.…

Although Breadth-First Search (BFS) has several advantages over Depth-First Search (DFS) its prohibitive space requirements have meant that algorithm designers often pass it over in favor of DFS. To address this shortcoming, we introduce a…

We present the first polynomial-time approximation schemes (PTASes) for the following subset-connectivity problems in edge-weighted graphs of bounded genus: Steiner tree, low-connectivity survivable-network design, and subset TSP. The…

The main results of this paper provide an Efficient Polynomial-Time Approximation Scheme (EPTAS) for approximating the genus (and non-orientable genus) of dense graphs. By dense we mean that $|E(G)|\ge \alpha |V(G)|^2$ for some fixed…

Many algorithms have been developed for NP-hard problems on graphs with small treewidth $k$. For example, all problems that are expressable in linear extended monadic second order can be solved in linear time on graphs of bounded treewidth.…

A searcher is tasked with exploring a graph with edge lengths and vertex weights, starting from a designated vertex. Initially, only the starting vertex is considered explored. At each step, the searcher adds an edge to the solution,…

In the Partially Embedded Planarity problem, we are given a graph $G$ together with a topological drawing of a subgraph $H$ of $G$. The task is to decide whether the drawing can be extended to a drawing of the whole graph such that no two…

We study the parameterized complexity of various classic vertex-deletion problems such as Odd cycle transversal, Vertex planarization, and Chordal vertex deletion under hybrid parameterizations. Existing FPT algorithms for these problems…

We revisit two well-studied problems, Bounded Degree Vertex Deletion and Defective Coloring, where the input is a graph $G$ and a target degree $\Delta$ and we are asked either to edit or partition the graph so that the maximum degree…

Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…