Given a complete graph on n nodes with metric edge costs, the minimum-cost khop spanning tree (kHMST) problem asks for a spanning tree of minimum total cost such that the longest root-leaf-path in the tree has at most k edges. We present an algorithm that computes such a tree of total expected cost O(log n) times that of a minimum-cost k-hop spanning-tree.

We conduct an extensive numerical analysis of the effects of network damage on dominating sets that occur at either randomly selected nodes or at the highest-degree nodes, in synthetic scale-free and real complex networks. We focus on the fraction of nodes that remain dominated after the damage has occurred, defined as stability. We find that minimum dominating sets (MDS), despite being optimal...

Untethered nodes in mobile ad-hoc networks strongly depend on the efficient use of their batteries. In this paper we propose a new metric, the drain rate, to forecast the lifetime of nodes according to current traffic conditions. This metric is combined with the value of the remaining battery capacity to determine which nodes can be part of an active route. We describe new route selection mecha...

In broadcasting, or one-to-all communication, a message originally held in one node of the network must be transmitted to all the other nodes. A minimal broadcast network is a communication network that can transmit a message originated at any node to all other nodes of the network in minimum time. In this paper, we present a compound method to construct sparse, time-relaxed, minimal broadcast ...

We investigate the uncertain versions of two classical combinatorial optimization problems, namely the Single-Pair Shortest Path Problem (SP-SPP) and the Single-Source Shortest Path Problem (SS-SPP). The former consists of finding a path of minimum length connecting two specific nodes in a finite directed graph G; the latter consists of finding the shortest paths from a fixed node to the remain...

The following algorithm partitions road networks surprisingly well: (i) sort the vertices by longitude (or latitude, or some linear combination) and (ii) compute the maximum flow from the first k nodes (forming the source) to the last k nodes (forming the sink). Return the corresponding minimum cut as an edge separator (or recurse until the resulting subgraphs are sufficiently small).

In this paper, we study a minimum connected dominating set problem (CDS) in wireless networks, which selects a minimum CDS with property that all intermediate nodes inside every pairwise shortest path should be included. Such a minimum CDS (we name this problem as SPCDS) is an important tache of some other algorithms for constructing a minimum CDS. We prove that finding such a minimum SPCDS can...

Multicast routing problem is to find a tree rooted at a source node to all multicast destination nodes. In dominating set problem, we are required to find a minimum size subset of vertices that each vertex is either in the dominating set or adjacent to some node in the dominating set. In this paper, we concentrate on the related problem of finding a connected dominating set of minimum size in w...

Many networks in real-life typically contain parts in which some nodes are more highly connected to each other than the other nodes of the network. The collection of such nodes are usually called clusters, communities, cohesive groups or modules. In graph terminology, it is called highly connected graph. In this paper, we first prove some properties related to highly connected graph. Based on t...

Wireless multicast/broadcast sessions, unlike wired networks, inherently reaches several nodes with a single transmission. For omnidirectional wireless broadcast to a node, all nodes closer will also be reached. Heuristic algorithms for constructing the minimum power tree in wireless networks have been proposed by Wieselthier et al. and Stojmenovic et al. Recently, an evolutionary search proced...