Harmender Gahlawat

Ben-Gurion University of the Negev | bgu · Department of Computer Science

The geodetic closure of a set S of vertices of a graph is the set of all vertices in shortest paths between pairs of vertices of S. A set S of vertices in a graph is geodetic if its geodetic closure contains all the vertices of the graph. Buckley introduced in 1984 the idea of a game where two players construct together a geodetic set by alternatel...

Cops and Robber is a well-studied two-player pursuit-evasion game played on a graph, where a group of cops tries to capture the robber. The \emph{cop number} of a graph is the minimum number of cops required to capture the robber. Gaven\v{c}iak et al.~[Eur. J. of Comb. 72, 45--69 (2018)] studied the game on intersection graphs and established that...

Decision trees is a fundamental tool in machine learning for representing, classifying, and generalizing data. It is desirable to construct ``small'' decision trees, by minimizing either the size (s) or the depth (d) of the decision tree (DT). Recently, the parameterized complexity of Decision Tree Learning has attracted a lot of attention. We cons...

The Hunters and Rabbit game is played on a graph G where the Hunter player shoots at k vertices in every round while the Rabbit player occupies an unknown vertex and, if it is not shot, must move to a neighbouring vertex after each round. The Rabbit player wins if it can ensure that its position is never shot. The Hunter player wins otherwise. The...

\textit{Pursuit-evasion games} have been intensively studied for several decades due to their numerous applications in artificial intelligence, robot motion planning, database theory, distributed computing, and algorithmic theory. \textsc{Cops and Robber} (\CR) is one of the most well-known pursuit-evasion games played on graphs, where multiple \te...

\textsc{Cops and Robber} is one of the most studied two-player pursuit-evasion games played on graphs, where multiple \textit{cops}, controlled by one player, pursue a single \textit{robber}. The main parameter of interest is the \textit{cop number} of a graph, which is the minimum number of cops that can ensure the \textit{capture} of the robber....

Graph Searching games are extensively studied in the literature for their vast number of applications in artificial intelligence, robot motion planning, game planning, distributed computing, and graph theory. In particular, Cops and Robber is one of the most well-studied graph searching game, where a set of cops try to capture the position of a sin...

Let G(V,E,c,w) be a weighted graph with vertex set V, edge set E, vertex-capacity function c:V→R+, and edge-weight function w:E→R+. In Bumblebee visitation problem, a mobile agent Bumblebee, denoted by B, begins by entering a vertex of the graph, and then moves along the edges of the graph. When B moves along an edge e=uv, both c(u) and c(v) are de...

Cops and Robber is a two-player pursuit-evasion game in which a set of cops, controlled by Player 1, try to capture the robber, controlled by Player 2. We study three models of this game on oriented graphs which differ based on the kind of moves the players can make. These models are (i) the normal cop model, where both cops and robber can only mov...

Cops and robber is a well-studied two player pursuit-evasion game played on a graph. In this game, a set of cops, controlled by the first player, tries to capture the position of a robber, controlled by the second player. The cop number of a graph is the minimum number of cops required to capture the robber in the graph. We show that the cop number...

We study the complexity of finding the \emph{geodetic number} on subclasses of planar graphs and chordal graphs. A set $S$ of vertices of a graph $G$ is a \emph{geodetic set} if every vertex of $G$ lies in a shortest path between some pair of vertices of $S$. The \textsc{Minimum Geodetic Set (MGS)} problem is to find a geodetic set with minimum car...

Cops and robber is a two player turn-based game played on a graph where cops try to capture the robber. The cop number of a graph is the minimum number of cops required to capture the robber. We consider two variants of this game, namely cops and attacking robber and lazy cops and robber. In cops and attacking robber version, the robber can attack...

In this paper, we study the computational complexity of finding the geodetic number of graphs. A set of vertices S of a graph G is a geodetic set if any vertex of G lies in some shortest path between some pair of vertices from S. The Minimum Geodetic Set (MGS) problem is to find a geodetic set with minimum cardinality. In this paper, we prove that...

In this paper, we study the computational complexity of finding the \emph{geodetic number} of graphs. A set of vertices $S$ of a graph $G$ is a \emph{geodetic set} if any vertex of $G$ lies in some shortest path between some pair of vertices from $S$. The \textsc{Minimum Geodetic Set (MGS)} problem is to find a geodetic set with minimum cardinality...

Cops and robber game on a directed graph \(\overrightarrow{D}\) initiates by Player 1 placing k cops and then Player 2 placing one robber on the vertices of \(\overrightarrow{D}\). After that, starting with Player 1, alternately the players may move each of their tokens to the adjacent vertices. Player 1 wins if, after a finite number of moves, a c...