The domatic partition problem seeks to maximize the partitioning of the nodes of the network into disjoint dominating sets. These sets represent a series of virtual backbones for wireless sensor networks to be activated successively, resulting in more balanced energy consumption and increased network robustness. In this study, we address the domatic partition problem in random geometric graphs ...

A graph is well-indumatched if all its maximal induced matchings are of the same size. We first prove that recognizing the class WIM of well-indumatched graphs is a co-NPcomplete problem even for (2P5,K1,5)-free graphs. We then show that the well-known decision problems such as Independent Dominating Set, Independent Set, and Dominating Set are NP-complete for well-indumatched graphs. We also s...

The idea of virtual backbone routing for ad hoc wireless networks is to operate routing protocols over a virtual backbone. One purpose of virtual backbone routing is to alleviate the serious broadcast storm problem suffered by many exiting on-demand routing protocols for route detection. Thus constructing a virtual backbone is very important. In our study, the virtual backbone is approximated b...

In this paper we present an algorithm with O(n log2n) complexity to find a shortest maximal increasing subsequence of a sequence of numbers. As a byproduct of this algorithm a O(n log2n) algorithm to find a minimum (weight) independent dominating set in permutation graphs is obtained, this compares favorable with the previous O(n3) algorithms known to solve

This paper presents distributed self-stabilizing algorithms for the maximal independent and the minimal dominating set problems. Using an unfair distributed scheduler the algorithms stabilizes in at most max{3n− 5,2n} resp. 9n moves. All previously known algorithms required O(n2) moves. © 2007 Elsevier B.V. All rights reserved.

In this paper, we study lower bounds for randomized solutions to the maximal independent set (MIS) and connected dominating set (CDS) problems in the dual graph model of radio networks—a generalization of the standard graph-based model that now includes unreliable links controlled by an adversary. We begin by proving that a natural geographic constraint on the network topology is required to so...

In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...

The five simple exceptional complex Lie superalgebras of vector fields are described. One of them, kas, is new; the other four are explicitly described for the first time. All nonisomorphic maximal subalgebras of finite codimension of these Lie superalgebras, i.e., all other realizations of these Lie superalgebras as Lie superalgebras of vector fields, are also described; there are 14 of them a...