Related papers: Optimal Tree for Both Synchronizability and Conver…
Sparse structures are frequently sought when pursuing tractability in optimization problems. They are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present.…
We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the…
Deciding whether there is a single tree -a supertree- that summarizes the evolutionary information in a collection of unrooted trees is a fundamental problem in phylogenetics. We consider two versions of this question: agreement and…
In deadline-constrained data aggregation in wireless sensor networks (WSNs), the imposed sink deadline along with the interference constraint hinders participation of all sensor nodes in data aggregation. Thus, exploiting the wisdom of the…
The aim of this paper is to highlight and explore a traditional problem, which is the minimum spanning tree, and finding the shortest-path in network routing, by using Swarm Intelligence. This work to be considered as an investigation topic…
This paper considers the conjecture by Gr\"unbaum that every planar 3-connected graph has a spanning tree $T$ such that both $T$ and its co-tree have maximum degree at most 3. Here, the co-tree of $T$ is the spanning tree of the dual…
We give polynomial time logarithmic approximation guarantees for the budget minimization, as well as for the profit maximization versions of minimum spanning tree interdiction. In this problem, the goal is to remove some edges of an…
A connected graph has tree-depth at most $k$ if it is a subgraph of the closure of a rooted tree whose height is at most $k$. We give an algorithm which for a given $n$-vertex graph $G$, in time $\mathcal{O}(1.9602^n)$ computes the…
Given a connected, undirected graph whose edges are labelled (or coloured), the minimum labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest number of distinct labels (or colours). In recent work, the…
We consider the message complexity of verifying whether a given subgraph of the communication network forms a tree with specific properties both in the KT-$\rho$ (nodes know their $\rho$-hop neighborhood, including node IDs) and the KT-$0$…
We propose an univesal scheme to design loop-free and super-stabilizing protocols for constructing spanning trees optimizing any tree metrics (not only those that are isomorphic to a shortest path tree). Our scheme combines a novel…
This paper studies coordination problem for time-varying networks suffering from antagonistic information, quantified by scaling parameters. By such a manner, interacting property of the participating individuals and antagonistic…
The inevitable random frequency differences among semiconductor lasers present an obstacle to achieving their collective coherence, but previous worked showed that fully (all-to-all) coupled networks can still be synchronized even in the…
Natural and man-made networks often possess locally tree-like sub-structures. Taking such tree networks as our starting point, we show how the addition of links changes the synchronization properties of the network. We focus on two…
This paper makes two main contributions: The first is the construction of a near-minimum spanning tree with constant average distortion. The second is a general equivalence theorem relating two refined notions of distortion: scaling…
In the length-constrained minimum spanning tree (MST) problem, we are given an $n$-node edge-weighted graph $G$ and a length constraint $h \geq 1$. Our goal is to find a spanning tree of $G$ whose diameter is at most $h$ with minimum…
We consider minimum-cost spanning trees, both in lattice and Euclidean models, in d dimensions. For the cost of the optimum tree in a box of size L, we show that there is a correction of order L^theta, where theta < 0 is a universal…
Network optimization strategies for the process of synchronization have generally focused on the re-wiring or re-weighting of links in order to: (1) expand the range of coupling strengths that achieve synchronization, (2) expand the basin…
The circumference of a graph $G$ is the length of a longest cycle in $G$, or $+\infty$ if $G$ has no cycle. Birmel\'e (2003) showed that the treewidth of a graph $G$ is at most its circumference minus $1$. We strengthen this result for…
The competition between local and global driving forces is significant in a wide variety of naturally occurring branched networks. We have investigated the impact of a global minimization criterion versus a local one on the structure of…