Related papers: A PTAS for vertex guarding weakly-visible polygons…
Given a simple polygon $\cal P$, in the Art Gallery problem, the goal is to find the minimum number of guards needed to cover the entire $\cal P$, where a guard is a point and can see another point $q$ when $\overline{pq}$ does not cross…
We study polynomial-time approximation schemes (PTASes) for constraint satisfaction problems (CSPs) such as Maximum Independent Set or Minimum Vertex Cover on sparse graph classes. Baker's approach gives a PTAS on planar graphs,…
Edge-Geodetic Sets play a crucial role in network monitoring and optimization, wherein the goal is to strategically place monitoring stations on vertices of a network, represented as a graph, to ensure complete coverage of edges and…
The associahedron is a convex polytope whose face poset is based on nonintersecting diagonals of a convex polygon. In this paper, given an arbitrary simple polygon P, we construct a polytopal complex analogous to the associahedron based on…
A dominating set of a graph G(V, E) is a set of vertices D\subseteq V such that every vertex in V\D has a neighbor in D. An eternal dominating set extends this concept by placing mobile guards on the vertices of D. In response to an…
We give a parameterized algorithm for weighted vertex cover on graphs with maximum degree 3 whose time complexity is $O^*(1.402^t)$, where $t$ is the minimum size of a vertex cover of the input graph.
In this paper we use several of the key ideas from Bidimensionality to give a new generic approach to design EPTASs and subexponential time parameterized algorithms for problems on classes of graphs which are not minor closed, but instead…
In this article we consider the problem of finding the visibility set from a given point when the obstacles are represented as the level set of a given function. Although the visibility set can be computed efficiently by ray tracing, there…
Given a graph $G$ and a subset of vertices $S = \{w_1, \ldots, w_t\} \subseteq V(G)$, the multiset representation of a vertex $u\in V(G)$ with respect to $S$ is the multiset $m(u|S) = \{| d_G(u, w_1), \ldots, d_G(u, w_t) |\}$. A subset of…
We present two algorithms for the minimum feedback vertex set problem in planar graphs: an $O(n \log n)$ PTAS using a linear kernel and balanced separator, and a heuristic algorithm using kernelization and local search. We implemented these…
Treewidth is a useful tool in designing graph algorithms. Although many NP-hard graph problems can be solved in linear time when the input graphs have small treewidth, there are problems which remain hard on graphs of bounded treewidth. In…
Compacting orthogonal drawings is a challenging task. Usually algorithms try to compute drawings with small area or edge length while preserving the underlying orthogonal shape. We present a one-dimensional compaction algorithm that alters…
A subset S of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from S. Denote by \psi_k(G) the minimum cardinality of a k-path vertex cover in G. It is shown that the problem…
The theoretical models providing mathematical abstractions for several significant optimization problems in machine learning, combinatorial optimization, computer vision and statistical physics have intrinsic similarities. We propose a…
A defensive alliance in an undirected graph $G=(V,E)$ is a non-empty set of vertices $S$ satisfying the condition that every vertex $v\in S$ has at least as many neighbours (including itself) in $S$ as it has in $V\setminus S$. We consider…
A set $S\subseteq V$ is a dominating set of $G$ if every vertex in $V - S$ is adjacent to at least one vertex in $S$. The domination number $\gamma(G)$ of $G$ equals the minimum cardinality of a dominating set $S$ in $G$; we say that such a…
In this paper, we introduce the problem of Matroid-Constrained Vertex Cover: given a graph with weights on the edges and a matroid imposed on the vertices, our problem is to choose a subset of vertices that is independent in the matroid,…
The eternal vertex cover game is played between an attacker and a defender on an undirected graph $G$. The defender identifies $k$ vertices to position guards on to begin with. The attacker, on their turn, attacks an edge $e$, and the…
An eternal dominating set of a graph $G$ is a set of vertices (or "guards") which dominates $G$ and which can defend any infinite series of vertex attacks, where an attack is defended by moving one guard along an edge from its current…
A set $S$ of vertices of a graph is a defensive alliance if, for each element of $S$, the majority of its neighbours are in $S$. We study the parameterized complexity of the Defensive Alliance problem, where the aim is to find a minimum…