Related papers: Making Life More Confusing for Firefighters
In this letter we study the NP-complete vertex cover problem on finite connectivity random graphs. When the allowed size of the cover set is decreased, a discontinuous transition in solvability and typical-case complexity occurs. This…
The paper deals with the Feedback Vertex Set problem parameterized by the solution size. Given a graph $G$ and a parameter $k$, one has to decide if there is a set $S$ of at most $k$ vertices such that $G-S$ is acyclic. Assuming the…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
Computational simulations of wildfire spread typically employ empirical rate-of-spread calculations under various conditions (such as terrain, fuel type, weather). Small perturbations in conditions can often lead to significant changes in…
A \emph{resolving set} $R$ in a graph $G$ is a set of vertices such that every vertex of $G$ is uniquely identified by its distances to the vertices of $R$. Introduced in the 1970s, this concept has been since then extensively studied from…
In the problem Fault-Tolerant Path (FTP), we are given an edge-weighted directed graph G = (V, E), a subset U \subseteq E of vulnerable edges, two vertices s, t \in V, and integers k and \ell. The task is to decide whether there exists a…
Recently, there has been increasing interest and progress in improvising the approximation algorithm for well-known NP-Complete problems, particularly the approximation algorithm for the Vertex-Cover problem. Here we have proposed a…
Coverage path planning in a generic known environment is shown to be NP-hard. When the environment is unknown, it becomes more challenging as the robot is required to rely on its online map information built during coverage for planning its…
We study the computability and complexity of the exploration problem in a class of highly dynamic graphs: periodically varying (PV) graphs, where the edges exist only at some (unknown) times defined by the periodic movements of carriers.…
The overwhelming majority of survivable (fault-tolerant) network design models assume a uniform fault model. Such a model assumes that every subset of the network resources (edges or vertices) of a given cardinality $k$ may fail. While this…
We study a class of optimal allocation problems, including the well-known Bomber Problem, with the following common probabilistic structure. An aircraft equipped with an amount~$x$ of ammunition is intercepted by enemy airplanes arriving…
Eternal vertex cover problem is a variant of the classical vertex cover problem modeled as a two player attacker-defender game. Computing eternal vertex cover number of graphs is known to be NP-hard in general and the complexity status of…
The purpose of this tutorial is to help individuals use the \underline{FireCommander} game environment for research applications. The FireCommander is an interactive, probabilistic joint perception-action reconnaissance environment in which…
We consider the Dynamic Map Visitation Problem (DMVP), in which a team of agents must visit a collection of critical locations as quickly as possible, in an environment that may change rapidly and unpredictably during the agents'…
During the last 10 years it has become popular to study dynamic graph problems in a emergency planning or sensitivity setting: Instead of considering the general fully dynamic problem, we only have to process a single batch update of size…
A graph environment must be explored by a collection of mobile robots. Some of the robots, a priori unknown, may turn out to be unreliable. The graph is weighted and each node is assigned a deadline. The exploration is successful if each…
We consider the algorithmic complexity of recognizing bipartite temporal graphs. Rather than defining these graphs solely by their underlying graph or individual layers, we define a bipartite temporal graph as one in which every layer can…
We consider a patrolling game on a graph recently introduced by Alpern et al. (2011) where the Patroller wins if he is at the attacked node while the attack is taking place. This paper studies the periodic patrolling game in the case that…
The classes Delay-FPT and Total-FPT recently have been introduced into parameterized complexity in order to capture the notion of efficiently solvable parameterized enumeration problems. In this paper we focus on ordered enumeration and…