Related papers: Typical solution time for a vertex-covering algori…
In the load balancing problem, each node in a network is assigned a load, and the goal is to equally distribute the loads among the nodes, by preforming local load exchanges. While load balancing was extensively studied in static networks,…
We introduce the discrete-time treatment number of a graph, in which each vertex is in exactly one of three states at any given time-step: compromised, vulnerable, or treated. Our treatment number is distinct from other graph searching…
We introduce an algorithm which solves mean payoff games in polynomial time on average, assuming the distribution of the games satisfies a flip invariance property on the set of actions associated with every state. The algorithm is a…
We investigate the gap between theory and practice for exact branching algorithms. In theory, branch-and-reduce algorithms currently have the best time complexity for numerous important problems. On the other hand, in practice,…
The notion of graph covers is a discretization of covering spaces introduced and deeply studied in topology. In discrete mathematics and theoretical computer science, they have attained a lot of attention from both the structural and…
We develop an algorithm of polynomial time complexity to construct the Grushko decomposition of fundamental groups of graphs of free groups with cyclic edge groups. Our methods rely on analysing vertex links of certain CAT(0) square…
We give an algorithm that decides whether the bipartite crossing number of a given graph is at most $k$. The running time of the algorithm is upper bounded by $2^{O(k)} + n^{O(1)}$, where $n$ is the number of vertices of the input graph,…
We provide conditions that classify cover times for sequences of random walks on random graphs into two types: One type (Type 1) is the class of cover times that are of the order of the maximal hitting times scaled by the logarithm of the…
This study investigated typical performance of approximation algorithms known as belief propagation, greedy algorithm, and linear-programming relaxation for maximum coverage problems on sparse biregular random graphs. After using the cavity…
Dominators provide a general mechanism for identifying reconverging paths in graphs. This is useful for a number of applications in Computer-Aided Design (CAD) including signal probability computation in biased random simulation, switching…
Connected Vertex Cover is one of the classical problems of computer science, already mentioned in the monograph of Garey and Johnson. Although the optimization and decision variants of finding connected vertex covers of minimum size or…
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…
We present the quantum algorithm for the Longest Trail Problem. The problem is to search the longest edge-simple path for a graph with $n$ vertexes and $m$ edges. Here edge-simple means no edge occurs in the path twice, but vertexes can…
We investigate the hitting times of random walks on graphs, where a hitting time is defined as the number of steps required for a random walker to move from one node to another. While much of the existing literature focuses on calculating…
Random walks on graphs are an essential primitive for many randomised algorithms and stochastic processes. It is natural to ask how much can be gained by running $k$ multiple random walks independently and in parallel. Although the cover…
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…
This study considers the (soft) capacitated vertex cover problem in a dynamic setting. This problem generalizes the dynamic model of the vertex cover problem, which has been intensively studied in recent years. Given a dynamically changing…
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
Joint time-vertex graph signals are pervasive in real-world. This paper focuses on the fundamental problem of sampling and reconstruction of joint time-vertex graph signals. We prove the existence and the necessary condition of a critical…
The Grundy number of a graph is the maximum number of colors used by the greedy coloring algorithm over all vertex orderings. In this paper, we study the computational complexity of GRUNDY COLORING, the problem of determining whether a…