相关论文: Solution to some conjectures on mobile position pr…

We study the problem of planning the deployments of a group of mobile robots. While the problem and formulation can be used for many different problems, here we use a bridge inspection as the motivating application for the purpose of…

Let $G=(V, E)$ be a graph where $V$ and $E$ are the vertex and edge sets, respectively. For two disjoint subsets $A$ and $B$ of $V$, we say $A$ \emph{dominates} $B$ if every vertex of $B$ is adjacent to at least one vertex of $A$. A vertex…

Corporate mobility is often based on a fixed assignment of vehicles to employees. Relaxing this fixation and including alternatives such as public transportation or taxis for business and private trips could increase fleet utilization and…

In this work, we consider the spatial search for a general marked state on graphs by continuous time quantum walks. As a simplest case, we compute the amplitude expression of the search for the multi-vertex uniform superposition state on…

We study the algorithmic problem of optimally covering a tree with $k$ mobile robots. The tree is known to all robots, and our goal is to assign a walk to each robot in such a way that the union of these walks covers the whole tree. We…

The general position number ${\rm gp}(G)$ of a connected graph $G$ is the cardinality of a largest set $S$ of vertices such that no three distinct vertices from $S$ lie on a common geodesic; such sets are refereed to as gp-sets of $G$. The…

The strong geodetic problem is to find the smallest number of vertices such that by fixing one shortest path between each pair, all vertices of the graph are covered. In this paper we study the strong geodetic problem on complete bipartite…

Motivated by dynamic graph visualization, we study the problem of representing a graph $G$ in the form of a \emph{storyplan}, that is, a sequence of frames with the following properties. Each frame is a planar drawing of the subgraph of $G$…

The K-way vertex cut problem} consists in, given a graph G, finding a subset of vertices of a given size, whose removal partitions G into the maximum number of connected components. This problem has many applications in several areas. It…

This paper addresses the mutual visibility problem for a set of semi-synchronous, opaque robots occupying distinct positions in the Euclidean plane. Since robots are opaque, if three robots lie on a line, the middle robot obstructs the…

Evolution of large scale networks demand for efficient way of communication in the networks. One way to propagate information in the network is to find vertex cover. In this paper we describe a variant of vertex cover problem naming it…

In the geodetic convexity, a set of vertices $S$ of a graph $G$ is $\textit{convex}$ if all vertices belonging to any shortest path between two vertices of $S$ lie in $S$. The cardinality $con(G)$ of a maximum proper convex set $S$ of $G$…

An autonomous mobile robot system consisting of many mobile computational entities (called robots) attracts much attention of researchers, and to clarify the relation between the capabilities of robots and solvability of the problems is an…

The concept of mutual-visibility (MV) has been extended in several directions. A vertex subset $S$ of a graph $G$ is a $k$-distance mutual-visibility ($k$DMV) set if for any two vertices in $S$, there is a geodesic between them of length at…

We study the communication complexity of the Minimum Vertex Cover (MVC) problem on general graphs within the \(k\)-party one-way communication model. Edges of an arbitrary \(n\)-vertex graph are distributed among \(k\) parties. The…

Learning heuristics for vehicle routing problems (VRPs) has gained much attention due to the less reliance on hand-crafted rules. However, existing methods are typically trained and tested on the same task with a fixed size and distribution…

A $t$-bar visibility representation of a graph assigns each vertex up to $t$ horizontal bars in the plane so that two vertices are adjacent if and only if some bar for one vertex can see some bar for the other via an unobstructed vertical…

The cage problem concerns finding $(k,g)$-graphs, which are $k$-regular graphs with girth $g$, of the smallest possible number of vertices. The central goal is to determine $n(k,g)$, the minimum order of such a graph, and to identify…

A maximal geodesic in a graph is a geodesic (alias shortest path) which is not a subpath of a longer geodesic. The geodesic-transversal problem in a graph $G$ is introduced as the task to find a smallest set $S$ of vertices of $G$ such that…

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…