Related papers: ETH-Hardness of Approximating 2-CSPs and Directed …
In recent years, much attention has been placed on the complexity of graph homomorphism problems when the input is restricted to ${\mathbb P}_k$-free and ${\mathbb P}_k$-subgraph-free graphs. We consider the directed version of this…
The 2-Edge-Connected Spanning Subgraph Problem (2ECSS) is a fundamental problem in survivable network design. Given an undirected $2$-edge-connected graph, the goal is to find a $2$-edge-connected spanning subgraph with the minimum number…
The problem of finding a maximum $2$-matching without short cycles has received significant attention due to its relevance to the Hamilton cycle problem. This problem is generalized to finding a maximum $t$-matching which excludes specified…
In the \emph{budgeted rooted node-weighted Steiner tree} problem, we are given a graph $G$ with $n$ nodes, a predefined node $r$, two weights associated to each node modelling costs and prizes. The aim is to find a tree in $G$ rooted at $r$…
We prove new results for approximating the graphic TSP and some related problems. We obtain polynomial-time algorithms with improved approximation guarantees. For the graphic TSP itself, we improve the approximation ratio to 7/5. For a…
In the field of constraint satisfaction problems (CSP), promise CSPs are an exciting new direction of study. In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the associated decision problem one must…
The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of…
The Parameterized Inapproximability Hypothesis (PIH) is the analog of the PCP theorem in the world of parameterized complexity. It asserts that no FPT algorithm can distinguish a satisfiable 2CSP instance from one which is only…
The minimum-weight $2$-edge-connected spanning subgraph (2-ECSS) problem is a natural generalization of the well-studied minimum-weight spanning tree (MST) problem, and it has received considerable attention in the area of network design.…
Connected Submodular Maximization (CSM) is a graph problem with important applications to wireless network deployment, path planning, epidemic outbreaks, and cancer genome studies. In CSM, we are given a graph $G$, a non-negative monotone…
Bl\"omer and Seifert showed that $\mathsf{SIVP}_2$ is NP-hard to approximate by giving a reduction from $\mathsf{CVP}_2$ to $\mathsf{SIVP}_2$ for constant approximation factors as long as the $\mathsf{CVP}$ instance has a certain property.…
For a given graph $G=(V,\, E)$ with a terminal set $S$ and a selected root $r\in S$, a positive integer cost and a delay on every edge and a delay constraint $D\in Z^{+}$, the shallow-light Steiner tree (\emph{SLST}) problem is to compute a…
We consider the problem of enumerating all minimal transversals (also called minimal hitting sets) of a hypergraph $\mathcal{H}$. An equivalent formulation of this problem known as the \emph{transversal hypergraph} problem (or…
We study the approximability of the NP-complete \textsc{Maximum Minimal Feedback Vertex Set} problem. Informally, this natural problem seems to lie in an intermediate space between two more well-studied problems of this type:…
Let $G$ be a strongly connected directed graph. We consider the following three problems, where we wish to compute the smallest strongly connected spanning subgraph of $G$ that maintains respectively: the $2$-edge-connected blocks of $G$…
We study the complexity of graph problems on graphs defined on groups, especially power graphs. We observe that an isomorphism invariant problem, such as Hamiltonian Path, Partition into Cliques, Feedback Vertex Set, Subgraph Isomorphism,…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
The problem of matching a query string to a directed graph, whose vertices are labeled by strings, has application in different fields, from data mining to computational biology. Several variants of the problem have been considered,…
We address the fundamental network design problem of constructing approximate minimum spanners. Our contributions are for the distributed setting, providing both algorithmic and hardness results. Our main hardness result shows that an…
In the Steiner Tree Augmentation Problem (STAP), we are given a graph $G = (V,E)$, a set of terminals $R \subseteq V$, and a Steiner tree $T$ spanning $R$. The edges $L := E \setminus E(T)$ are called links and have non-negative costs. The…