Related papers: Broadcasting under Structural Restrictions
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…
In this paper, we address the problem of broadcasting in a wireless network under a novel communication model: the {\em swamping} communication model. In this model, nodes communicate only with those nodes at geometric distance greater than…
A secure set $S$ in a graph is defined as a set of vertices such that for any $X\subseteq S$ the majority of vertices in the neighborhood of $X$ belongs to $S$. It is known that deciding whether a set $S$ is secure in a graph is…
Let $G=(V,E)$ be a graph and $t,r$ be positive integers. The \emph{signal} that a tower vertex $T$ of signal strength $t$ supplies to a vertex $v$ is defined as $sig(T,v)=max(t-dist(T,v),0),$ where $dist(T,v)$ denotes the distance between…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
The Virtual Network Embedding Problem (VNEP) considers the efficient allocation of resources distributed in a substrate network to a set of request networks. Many existing works discuss either heuristics or exact algorithms, resulting in a…
A line-broadcasting model in a connected graph $G=(V,E)$, $|V|=n$, is a model in which one vertex, called the {\it originator} of the broadcast holds a message that has to be transmitted to all vertices of the graph through placement of a…
A stable or locally-optimal cut of a graph is a cut whose weight cannot be increased by changing the side of a single vertex. In this paper we study Minimum Stable Cut, the problem of finding a stable cut of minimum weight. Since this…
We initiate the study of the parameterized complexity of the {\sc Collective Graph Exploration} ({\sc CGE}) problem. In {\sc CGE}, the input consists of an undirected connected graph $G$ and a collection of $k$ robots, initially placed at…
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…
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 consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge appears in the network with its associated…
Given a graph $G$ and an integer $k$, the Feedback Vertex Set (FVS) problem asks if there is a vertex set $T$ of size at most $k$ that hits all cycles in the graph. The fixed-parameter tractability status of FVS in directed graphs was a…
The Firefighting problem is defined as follows. At time $t=0$, a fire breaks out at a vertex of a graph. At each time step $t \geq 0$, a firefighter permanently defends (protects) an unburned vertex, and the fire then spread to all…
The interference at a wireless node s can be modelled by the number of wireless nodes whose transmission ranges cover s. Given a set of positions for wireless nodes, the interference minimization problem is to assign a transmission radius…
The message complexity of a distributed algorithm is the total number of messages sent by all nodes over the course of the algorithm. This paper studies the message complexity of distributed algorithms for fundamental graph optimization…
Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More…
In wireless networks, consisting of battery-powered devices, energy is a costly resource and most of it is spent on transmitting and receiving messages. Broadcast is a problem where a message needs to be transmitted from one node to all…
Multi-Robot Coverage problems have been extensively studied in robotics, planning and multi-agent systems. In this work, we consider the coverage problem when there are constraints on the proximity (e.g., maximum distance between the…
We obtain structure theorems for graphs excluding a fan (a path with a universal vertex) or a dipole ($K_{2,k}$) as a topological minor. The corresponding decompositions can be computed in FPT linear time. This is motivated by the study of…