In this chapter, a UDG-based greedy anti-void routing (GAR) protocol is proposed to re-solve the void problem incurred by the conventional green concept-based greedy forwarding algorithm. The rolling-ball UDG boundary traversal (RUT) scheme is adopted within the GAR protocol to solve the boundary finding problem, which results in guaranteed delivery of data packets under the UDG networks. The boundary map (BM) is also proposed to conquer the computational problem of the rolling mechanism in the RUT scheme, forming the direct mappings between the input/output nodes. The proposed indirect map searching (IMS) al-gorithm constructs the boundary map with the time and space complexities of O(m2) and O(m), where m represents the number of neighbors. The correctness of the RUT scheme, the GAR algorithm, and the time/space complexity of the IMS method is properly proven. The hop count reduction (HCR) and the intersection navigation (IN) mechanisms are proposed as the delay-reducing schemes for the GAR algorithm; while the partial UDG construction (PUC) mechanism is utilized to generate the required topology for the RUT scheme under the non-UDG networks. All these enhanced mechanisms associated with the GAR protocol are proposed as the enhanced GAR (GAR-E) algorithm that inherits the merit of guaranteed delivery. The performance of both the GAR and GAR-E protocols is evaluated via simula-tions and is compared with existing localized routing algorithms. The simulation study shows that the proposed GAR and GAR-E algorithms can guarantee the delivery of data packets under the UDG network; while the GAR-E scheme further improves the routing performance with reduced communication overhead under different network scenarios. These proposed GAR-based schemes can therefore be adopted as the unicast protocols in the green wireless access networks.
Chapter 3
Three-Dimensional Greedy Anti-Void Routing Protocol
Chapter Overview
In the network layer unicast protocol design for achieving the green wireless access networks, a greedy anti-void routing (GAR) protocol is proposed in the previous chapter. However, the proposed GAR scheme is mainly designed for the two dimensional network. In the three dimensional space, the unreachability problem (i.e., the so-called void problem) resulting from the low-overhead green concept-based greedy forwarding (GF) algorithm has not been fully resolved. In this chapter, a three-dimensional greedy anti-void routing (3D-GAR) protocol is proposed to solve the 3D void problem by exploiting the boundary finding technique for the unit ball graph (UBG) with the main theme of the wireless sensor network (WSN) since the WSN has stringent requirements on the energy saving issues. The proposed 3D rolling-ball UBG boundary traversal (3D-RUT) scheme is employed to guarantee the delivery of packets from the source to the destination node. The correctness proofs, protocol implementation, and performance evaluation for the proposed 3D-GAR protocol are also given and properly explained. Based on the evaluation results, the proposed 3D-GAR protocol can guarantee the packet delivery and maintain comparably low routing overheads, which matches the unicast protocol design goal for achieving the green wireless access networks.
3.1 Introduction
In recent years, three-dimensional (3D) routing has gained attention in the wireless sensor networks (WSNs). For example, the applications for underwater sensor networks have be-come more popular in the field of oceanographic engineering, including data collection, water monitoring, pollution control, and ocean surveillance. Previous work on the routing proto-cols for the 3D WSNs can be found in [37]. Due to the limited available resources, efficient design of localized routing protocols becomes a crucial subject within the 3D WSNs. How to guarantee delivery of packets is considered an important issue for the localized routing algorithms. The well-known greedy forwarding (GF) protocol [4] is proposed as a superior scheme with its low routing overheads and the adaptability to the 3D-routing environment.
However, the unreachability problem (i.e., the so-called void problem [5]) occurring within the GF algorithm will fail to guarantee the delivery of data packets. In order to alleviate the void problem, the 3D-ABLAR protocol [38] employs the heuristic next-hop selection tech-niques that forward packets to additional two neighbor nodes located in separated regions so as to gain more chance to escape from the void. The projection from two-dimensional (2D) face routing to 3D space is also proposed in [39] as another technique to deal with the void problem. However, the void problem resulting from the GF algorithm has not been fully resolved under the 3D environment. In this chapter, a 3D greedy anti-void routing (3D-GAR) protocol is proposed to solve the void problem under the unit ball graph (UBG) settings.
The associated three-dimensional rolling-ball UBG boundary traversal (3D-RUT) scheme is exploited within the 3D-GAR algorithm with the assurance for packet delivery. Moreover, the proofs of correctness, protocol implementation, and performance evaluation for the proposed algorithms are also given and properly described.
The remainder of this chapter is organized as follows. Section 3.2 describes the network model and the problem statement. The proposed 3D-GAR protocol and the corresponding proofs of correctness are explained in Section 3.3. Section 3.4 provides the protocol imple-mentation; while the performance evaluation is conducted and compared with other existing schemes in Section 3.5. Section 3.6 summarizes this chapter.
SV
Figure 3.1: The example routing path constructed by using the 3D-GAR algorithm.
3.2 Network Model and Problem Statement
Considering a set of SNs N = {Ni| ∀ i} within a 3D Euclidean space R3, the locations of the set N are represented by the set P = {PNi| PNi = (xNi, yNi, zNi), ∀i}, which can be acquired by their own positioning systems. The set of closed balls defining the transmission ranges of N is denoted as Θ = {Θ(PNi, R) | ∀ i}, where Θ(PNi, R) = {x | kx − PNik ≤ R, ∀ x ∈ R3}. It is noted that PNi is the center of the closed ball with R denoted as the radius of the transmission range for each Ni. Furthermore, a unit ball graph (UBG) is defined as the intersection graph of a group of unit spheres in R3. Therefore, the network model for the 3D WSNs can be represented by a 3D UBG as G(P, E) with the edge set E = {Eij| Eij = (PNi, PNj), PNi ∈ Θ(PNj, R), ∀ i 6= j}. The edge Eij indicates the unidirectional link from PNi to PNj whenever the position PNi is within the closed ball region Θ(PNj, R).
Moreover, the one-hop neighbor table for each Ni is defined as TNi = {[IDNk, PNk] | PNk ∈ Θ(PNi, R), ∀ k 6= i}, where IDNk represents the designated identification number for Nk. In the greedy forwarding (GF) algorithm, it is assumed that the source node NS is aware of the
location of the destination node ND. If NS wants to transmit packets to ND, it will choose the next hop from its TNS which (a) has the shortest Euclidean distance to ND among all the SNs in TNS and (b) is located closer to ND compared to the distance between NS and ND. The same procedure will be performed by the intermediate nodes (e.g., NV as in Fig. 3.1) until ND is reached. However, the GF algorithm will be inclined to fail due to the occurrences of voids even though some routing paths exist from NS to ND. The void problem is defined as follows:
Problem 4 (Void Problem). The greedy forwarding (GF) algorithm is exploited for packet delivery from NS to ND. The void problem occurs while there exists a void node (NV) in the network such that
{PNk| d(PNk, PND) < d(PNV, PND), ∀ PNk ∈ TNV} = ∅, (3.1)
where d(x, y) represents the Euclidean distance between x and y. TNV is the one-hop neighbor table of NV.