Related papers: A Self-Stabilizing Minimal k-Grouping Algorithm

For a finite group $G$, the size of a minimum generating set of $G$ is denoted by $d(G)$. Given a finite group $G$ and an integer $k$, deciding if $d(G)\leq k$ is known as the minimum generating set (MIN-GEN) problem. A group $G$ of order…

The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes…

We propose a self-stabilizing algorithm for computing a maximal matching in an anonymous network. The complexity is $O(n^3)$ moves with high probability, under the adversarial distributed daemon. In this algorithm, each node can determine…

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,…

A minimal separator of a graph $G$ is a set $S \subseteq V(G)$ such that there exist vertices $a,b \in V(G) \setminus S$ with the property that $S$ separates $a$ from $b$ in $G$, but no proper subset of $S$ does. For an integer $k\ge 0$, we…

We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…

The component size of a graph is the maximum number of edges in any connected component of the graph. Given a graph $G$ and two integers $k$ and $c$, $(k,c)$-Decomposition is the problem of deciding whether $G$ admits an edge partition into…

In the problem of minimum connected dominating set with routing cost constraint, we are given a graph $G=(V,E)$, and the goal is to find the smallest connected dominating set $D$ of $G$ such that, for any two non-adjacent vertices $u$ and…

In this paper, we present, to our knowledge, the first known I/O efficient solutions for computing the k-bisimulation partition of a massive directed graph, and performing maintenance of such a partition upon updates to the underlying…

Let ${\cal G}$ be a minor-closed graph class and let $G$ be an $n$-vertex graph. We say that $G$ is a $k$-apex of ${\cal G}$ if $G$ contains a set $S$ of at most $k$ vertices such that $G\setminus S$ belongs to ${\cal G}$. Our first result…

We present a \emph{deterministic exact algorithm} for the \emph{minimum $k$-cut problem} on simple graphs. Our approach combines the \emph{principal sequence of partitions (PSP)}, derived canonically from ideal loads, with a single level of…

Given a graph $G=(V,E)$ and an integer $k \ge 1$, a $k$-hop dominating set $D$ of $G$ is a subset of $V$, such that, for every vertex $v \in V$, there exists a node $u \in D$ whose hop-distance from $v$ is at most $k$. A $k$-hop dominating…

To address the issue of excessive quantum resource requirements in Kuperberg's algorithm for the dihedral hidden subgroup problem, this paper proposes a distributed algorithm based on the function decomposition. By splitting the original…

In this paper, we study the {\sc Dominating Set} problem in random graphs. In a random graph, each pair of vertices are joined by an edge with a probability of $p$, where $p$ is a positive constant less than $1$. We show that, given a…

In this paper we study the problem of testing graph isomorphism (GI) in the CONGEST distributed model. In this setting we test whether the distributive network, $G_U$, is isomorphic to $G_K$ which is given as an input to all the nodes in…

A set $S\subseteq V$ of a graph $G=(V,E)$ is a dominating set if each vertex has a neighbor in $S$ or belongs to $S$. Dominating Set is the problem of deciding, given a graph $G$ and an integer $k\geq 1$, if $G$ has a dominating set of size…

In computer networks, participants may cooperate in processing tasks, so that loads are balanced among them. We present local distributed algorithms that (repeatedly) use local imbalance criteria to transfer loads concurrently across the…

In the k-Disjoint Shortest Paths problem, a set of terminal pairs of vertices $\{(s_i,t_i)\mid 1\le i\le k\}$ is given and we are asked to find paths $P_1,\ldots,P_k$ such that each path $P_i$ is a shortest path from $s_i$ to $t_i$ and…

Self-stabilizing algorithms are an important because of their robustness and guaranteed convergence. Starting from any arbitrary state, a self-stabilizing algorithm is guaranteed to converge to a legitimate state.Those algorithms are not…

Consider the family of graphs without $ k $ node-disjoint odd cycles, where $ k $ is a constant. Determining the complexity of the stable set problem for such graphs $ G $ is a long-standing problem. We give a polynomial-time algorithm for…