International Journal of Foundations of Computer Science

Cellular communications has experienced an explosive growth recently. In order to increase the capacity of a cellular network without new frequency spectrum allocation, it is a common practice to use base stations with a lower power transmitter. Cell splitting is one of such techniques, which increases the network capacity four-fold by dividing a cell into four smaller cells. Although the cell splitting technique can reuse the existing base stations, it requires that those existing base stations be uniformly distributed. In addition, the radius of each new cell is always half that of the original cell. In this paper, it is assumed that the radius of new cells can be of any smaller size, and that the existing base stations are not necessarily uniformly distributed. While new base stations can be placed at the cell centers based on the design of the new cellular network, existing base stations should be put as close to a cell center as possible in the new cellular network. The problem to be solved, referred to as the optimal cellular network deployment, can be formulated as follows: given a set of existing base stations and a planned cellular network that has a fixed cell size and network orientation but is movable, find a position to fix the movable cellular network such that the maximum distance between existing base stations and their corresponding cell centers is minimized. This paper shows that the optimal cellular network deployment problem can be solved in O(n³) time if n existing base stations will be reused.

In this paper, we review some new distributed algorithms that construct sparse subgraphs with bounded degree of the unit disk graph efficiently for wireless ad hoc networks. They maintain a linear number of links while still preserving power-efficient routes for any pair of nodes. It was open whether the Yao plus reverse Yao graph and the symmetric Yao graph are spanners. We show that the Yao plus reverse Yao graph has a bounded power stretch factor 2 in civilized unit disk graph. In addition, we review a recent example by M. Grünewald et al. [6] to show that the symmetric Yao graph does not have a constant bounded stretch factor. Finally, we conduct simulations to study the practical performances of these structures. All structures have small power stretch factors for randomly generated unit disk graphs in our experiments.

We propose a general framework for broadcasting in ad hoc networks through self-pruning. The approach is based on selecting a small subset of hosts (also called nodes) to form a forward node set on carry out a broadcast process. Each node, upon receiving a broadcast packet, determines whether to forward the packet or not based on two neighborhood coverage conditions proposed in this paper. These coverage conditions depend on neighbor connectivity and history of visited nodes, and in general, resort to global network information. Using local information such as k-hop neighborhood information, the forward node set is selected through a distributed and local pruning process. The forward node set can be constructed and maintained through either a proactive process (i.e., "up-to-date") or a reactive process (i.e., "on-the-fly"). Several existing broadcast algorithms can be viewed as special cases of the coverage conditions with k-hop neighborhood information. Simulation results show that new algorithms, which are more efficient than existing ones, can be derived from the coverage conditions, and self-pruning based on 2- or 3-hop neighborhood information is relatively more cost-effective.

Mobile Backbone Wireless Networks (MBWN) [10] are wireless networks in which the base stations are mobile. Our strategy is the following: mobile nodes are dynamically grouped into clusters of bounded radius. In the very large wireless networks we deal with we deal with, several hundreds of clusters may be generated. Clustering makes use of a two dimensional Euclidean version of the Antipole Tree data structure [5]. This very effective structure was originally designed for finite sets of points in an arbitrary metric space to support efficient range searching. It requires only a linear number of pair-wise distance calculations among nodes. Mobile Base Stations occupy an approximate centroid of the clusters and are moved according to a fast practical bipartite matching algorithm which tries to minimize both total and maximum distance. We show that the best known computational geometry algorithms [1] become infeasible for our application when a high number of mobile base stations is required. On the other hand our proposed 8% average error solution requires O(k log k) running time instead of the approximatively O(k²) exact algorithm [1]. Communication among nodes is realized by a Clusterhead Gateway Switching Routing (CGSR) protocol [15] where the mobile base stations are organized in a suitable network. Other efficient clustering algorithms [11, 17] may be used instead of the Antipole Tree. However the nice hierarchical structure of the Antipole Tree makes it applicable to other types of mobile wireless (Ad-Hoc) and wired networks but this will be subject of future work.

This paper introduces Neighbor Aware Adaptive Power flooding, an optimized flooding mechanism used in mobile ad hoc networks (MANETS) that employs several mechanisms (neighbor coverage, power control, neighbor awareness and local optimization) to limit the broadcast storm problem, reduce duplicate packet reception and lower power consumption in both transmission and reception. Upon receiving an optimized broadcast, a relay determines a new set of possible relays (to continue the flood) based upon local neighbor information and the previous optimized broadcast. Additionally, neighboring relays only consider the shared neighbors they are closest to. A relay may perform local optimization (to reduce power consumption and isolate broadcasts) by substituting one high power broadcast with two or more low power broadcasts, thereby introducing additional hops, We show that compared to blind flooding and multipoint relaying, NAAP in a static environment greatly reduces the problems associated with the broadcast storm problem, duplicate packet reception and power consumption.

In this paper, we study broadcasting protocols where nodes use some of their neighbors to forward messages. We propose a new protocol based on a variant of neighbor elimination scheme using RNG graph to ensure a full coverage of the network. The computation of RNG uses two kinds of distance: a geometrical one and and neighborhood-based distance that permits to use our protocol without positioning system. This protocol, called RRS for RNG Relay Subset, provides a self-selecting forwarding neighbor operating mode which guarantees a fair broadcast loading. In RRS a node v is a relay for a node u if and only if v is a neighbor of u and v has a RNG-neighbor which is not covered by u transmission. Moreover, experiments with 802.11-like MAC layer show that RRS is efficient.

New technologies and the deployment of mobile and nomadic services are driving the emergence of complex communications networks, that have a highly dynamic behavior. This naturally engenders new route-discovery problems under changing conditions over these networks. Unfortunately, the temporal variations in the network topology are hard to be effectively captured in a classical graph model. In this paper, we use and extend a recently proposed graph theoretic model, which helps capture the evolving characteristic of such networks, in order to propose and formally analyze least cost journey (the analog of paths in usual graphs) in a class of dynamic networks, where the changes in the topology can be predicted in advance. Cost measures investigated here are hop count (shortest journeys), arrival date (foremost journeys), and time span (fastest journeys).

A maximal independent set (MIS) S for a graph G is an independent set and no proper superset of S is also independent. A set S is dominating if each node in the graph is either in S or adjacent to one of the nodes in S. The subgraph weakly induced by S is the graph G′ such that each edge in G′ has at least one end point in S. A set S is a weakly-connected dominating set (WCDS) of G if S is dominating and G′ is connected. G′ is a sparse spanner if it has linear edges. The nodes of WCDS have been proposed in the literature as clusterheads for clustered wireless ad hoc networks. In this paper, we present two distributed algorithms for constructing a WCDS for wireless ad hoc networks in linear time. The first algorithm has an approximation ratio of 5, and requires O(n log n) messages, while the second algorithm has a larger approximation ratio, and requires only O(n) messages. Both of these algorithms are used to obtain sparse spanners. The spanner obtained by the second algorithm has a topological dilation of 3, and a geometric dilation of 6. Both of these algorithms are based on the construction of a MIS. The first algorithm requires the construction of a spanning tree. The second algorithm is fully localized, and does not depend on the spanning tree, which makes the maintenance of the WCDS simpler, and guarantees the maintenance of the same approximation ratio.

A Mobile Ad Hoc Network (MANET) is an infrastructureless wireless network that can support highly dynamic mobile units. The multi-hop feature of a MANET suggests the use of clustering to simplify routing. Graph domination can be used in defining clusters in MANETs. A variant of dominating set which is more suitable for clustering MANETs is the weakly-connected dominating set. A cluster is defined to be the set of vertices dominated by a particular vertex in the dominating set. As it is NP-complete to determine whether a given graph has a weakly-connected dominating set of a particular size, we present a zonal distributed algorithm for finding small weakly-connected dominating sets. In this new approach, we divide the graph into regions, construct a weakly-connected dominating set for each region, and make adjustments along the borders of the regions to produce a weakly-connected dominating set of the entire graph. We present experimental evidence that this zonal algorithm has similar performance to and provides better cluster connectivity than previous algorithms.

Let α₂(G), γ(G) and γ_c(G) be the 2-independence number, the domination number, and the connected domination number of a graph G respectively. Then α₂(G) ≤ γ (G) ≤ γ_c(G). In this paper , we present a simple heuristic for Minimum Connected Dominating Set in graphs. When running on a graph G excluding K_m (the complete graph of order m) as a minor, the heuristic produces a connected dominating set of cardinality at most 7α₂(G) - 4 if m = 3, or at most if m ≥ 4. In particular, if running on a planar graph G, the heuristic outputs a connected dominating set of cardinality at most 15α₂(G) - 5.