相关论文: A Tractable Variant of Cover Time
The cover time of a finite connected graph is the expected number of steps needed for a simple random walk on the graph to visit all the vertices. It is known that the cover time on any n-vertex, connected graph is at least (1+o(1)) n…
A close relation between hitting times of the simple random walk on a graph, the Kirchhoff index, resistance-centrality, and related invariants of unicyclic graphs is displayed. Combining with the graph transformations and some other…
We introduce a cover time problem for random walks on dynamic graphs in which the graph expands in time and the walker moves at random times. Time to cover all nodes and number of returns to original states are analyzed in resulting model.
In the 4-path vertex cover problem, the input is an undirected graph $G$ and an integer $k$. The goal is to decide whether there is a set of vertices $S$ of size at most $k$ such that every path with 4 vertices in $G$ contains at least one…
We study a random walk that prefers tou se unvisited edges in the context of random cubic graphs. We establish asymptotically correct estimates for the vertex and edge cover times, these being $\approx n\log n$ and $\approx \frac32n\log n$…
We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…
In the PATH COVER problem, one asks to cover the vertices of a graph using the smallest possible number of (not necessarily disjoint) paths. While the variant where the paths need to be pairwise vertex-disjoint, which we call PATH…
A temporal graph is a graph whose edges only appear at certain points in time. Reachability in these graphs is defined in terms of paths that traverse the edges in chronological order (temporal paths). This form of reachability is neither…
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.
Given a traversal algorithm, cover time is the expected number of steps needed to visit all nodes in a given graph. A smaller cover time means a higher exploration efficiency of traversal algorithm. Although random walk algorithms have been…
The cover time of a finite connected graph is the expected number of steps needed for a simple random walk on the graph to visit all vertices of the graph. It is known that the cover time of any finite connected $n$-vertex graph is at least…
We consider extension variants of the classical graph problems Vertex Cover and Independent Set. Given a graph $G=(V,E)$ and a vertex set $U \subseteq V$, it is asked if there exists a minimal vertex cover (resp.\ maximal independent set)…
We compute the number of equivalence classes of nonperiodic covering cycles of given length in a non oriented connected graph. A covering cycle is a closed path that traverses each edge of the graph at least once. A special case is the…
A temporal graph is a graph in which the edge set can change from one time step to the next. The temporal graph exploration problem TEXP is the problem of computing a foremost exploration schedule for a temporal graph, i.e., a temporal walk…
In the $l$-path vertex cover problem the input is an undirected graph $G$ and an integer $k$. The goal is to decide whether there is a set of vertices $S$ of size at most $k$ such that $G-S$ does not contain a path with $l$ vertices. In…
Covering all edges of a graph by a small number of vertices, this is the NP-complete Vertex Cover problem. It is among the most fundamental graph-algorithmic problems. Following a recent trend in studying temporal graphs (a sequence of…
A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…
In the 3-path vertex cover problem, the input is an undirected graph $G$ and an integer $k$. The goal is to decide whether there is a set of vertices $S$ of size at most $k$ such that every path with 3 vertices in $G$ contains at least one…
We study spreading processes in temporal graphs, i. e., graphs whose connections change over time. These processes naturally model real-world phenomena such as infectious diseases or information flows. More precisely, we investigate how…
In any attempt at designing an efficient algorithm for the minimum vertex cover problem, obtaining good upper and lower bounds for the vertex cover number could be crucial. In this article we present a modified greedy algorithm of…