Chapter 3 Our Proposed Schemes
3.3 Steiner Trees Grid Routing Protocol
Before going further, let us first explain the network model in our work. As we have known that the main task of sink node is to disseminate the user queries into a sensor network and retrieve the corresponding data from the sensor network. For this purpose, a sensor network is assumed to have the following characteristics. The sensor field is made up of hundreds or perhaps thousands of small, cheap sensing devices that are randomly deployed throughout a two-dimensional area of interest.
The power supply is restricted due to the size of sensor nodes. Short-range radios with static transmission power are used due to the energy constraint. Therefore, multi-hop forwarding schemes are used to achieve long-range communication. The sensing devices are assumed to have a fixed and known location within the sensor field. An immobile data sink is deployed with the area of interest, and has location knowledge and an infinite power source.
Now, we are going to introduce our proposed routing scheme, which is called the Steiner Trees Grid Routing (STGR) protocol. In order to reduce the total energy consumption for data transmission between the source node and the sink node, we construct a different virtual grid structure instead of virtual grid in GGR. Our idea is to construct the virtual grid structure based on the square Steiner trees. In the following, we will first introduce the concept of Steiner trees. Then, our virtual grid structure will be explained.
The Steiner tree problem, created by Jakob Steiner, is a problem in combinatorial optimization. The Steiner tree problem is similar to the minimum spanning tree problem, but the difference between the Steiner problem and the minimum spanning tree is that, in the Steiner tree problem, extra intermediate vertices may be added to
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the graph in order to reduce the length of the spanning tree. These new vertices introduced to decrease the total length of connection are known as Steiner points [13].
The basic idea of our approach is using the grid routing which is based upon a square Steiner tree. In that way we need know how to add extra vertices in the grid.
Basis on [13], the Steiner point in a triangle is also a Fermat point. There are some ways to find Steiner point in a triangle form, shows in Figure 3.4, we can use any one side of a triangle to draw a regular triangle and circumscribe this regular triangle, just like two dashed lines in Figure 3.4. Two dashed lines will cross a point in original triangle, which is the Steiner point. In the Figure 3.5, points A, B and C connect with Steiner point P, become to a Steiner tree with three vertices. In view of Steiner tree with three points, we can use similar way to find a Steiner tree with four points.
Figure 3.6 shows that there is a square have two Steiner points X and Y by connected two vertices of circumscribed circle. So shows in Figure 3.7, points A, B, C and D connect with Steiner points which closest to itself, become a Steiner Tree.
A
B
C P
Figure 3.4. A Steiner Point P in a △ABC.
A
B
P
C
Figure 3.5. A Steiner tree with three points A, B and C.
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A
B C
D
X Y
Figure 3.6. Two Steiner Points X and Y in a square.
A
B C
D
X Y
Figure 3.7. A Steiner tree with four points A, B, C and D.
3.3.1 Network Construction
Once the sensor nodes are deployed in the sensor field, the sink node starts to construct the grid structure. The sink divides the plane into a grid of cells.
Cross-points of the grid are the Dissemination Points (DPs). The size of the cells, denoted as , is determined by the sink such that DPs are not within direct transmission range. The sink is the first DP. Knowing its own position and the size of each cell, the sink is able to send a data request (in the form of a data-announcement message) to each adjacent Dissemination Point in the grid. For a sink at location Ls=(x, y), dissemination points are located at Lp = (xi, yj) such that:
{𝑥𝑖 = 𝑥 + 𝑖 ∙ 𝛼, 𝑦𝑖 = 𝑦 + 𝑗 ∙ 𝛼; 𝑖, 𝑗 = ± 0, ± 1, ± 2 … }.
According to Figure 3.6, the positions of X and Y depends on the length of square, so Steiner Points (SP) are located at Lsp = (xi, yj) such that:
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{𝑥𝑖 = 𝑥 ± 𝑖 ∙ 3
6 𝛼, 𝑦𝑖 = 𝑦 ± 𝑗 ∙𝛼
2; 𝑖, 𝑗 = ± 0, ± 1, ± 2 … }
Simple geographic forwarding is used to reach these locations. Upon receiving the data-announcement message, the closest known sensor node to each DP and SP promotes itself to become a Dissemination Node (DN), and DN will record belong to which DP or SP. Then, the DN forwards the data-announcement message to each of its adjacent DPs and SPs, except the point from which the data-announcement message was received. These actions are repeated as the data-announcement message propagates and Dissemination Nodes are chosen throughout the sensor field. There is an example shown in Figure 3.8.
DNs for DPs Sink DNs for SPs
Figure 3.8. The network construction in STGR.
The data-announcement messages contain the additive hop count and used energy of DNs along the upstream path. Using this information, Dissemination Nodes store the most energy efficient upstream links toward the sink. An upstream is dropped if a lower or equal cost link can be offered to the neighboring Dissemination
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Node. The forwarding grid provides multiple paths toward the sink while avoiding routing loops.
3.3.2 Routing Phase
Any node that is within the target region of a received QUERY message stores the appropriate routing information and starts to send the sensed data (in the form of DATA message) to the sink. The routing information contains the appropriate upstream DNs through which DATA messages will be forwarded. DN choice which way to transmit DATA message depending on DN belong to DP or SP. If DN belongs to SP, DN will choose a upstream along the hexagon. There are two conditions if DN belongs to DP. While the location of DP, Lp = (xi, yj) wasn't parallel or vertical as the location of sink, Ls=(x, y). DN would choice the upstream along the hexagon.
Otherwise, DN would choice the upstream along the grid. As shown in Figure 3.9, DN transported data about the event A along the grid, and DN transported data about the event B along the hexagon.
DNs for DPs Sink DNs for SPs
Event A Event B
Figure 3.9. Routing paths in STGR.
Having established routing paths to the sinks through Dissemination Nodes, data forwarding process can be started. Data forwarding involves reception and forwarding
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of DATA messages, acknowledgment of those messages and reception of acknowledgments for messages sent. The acknowledgment messages sent between DNs are used to acknowledge DATA messages and for flow control. If a single link fails, the affected downstream DNs often have one or two spare upstream links that can be used instead. In addition to its use in increasing communication reliability, the acknowledgments for messages can be used in dealing with path failures. In the event that no more upstream links are available, an acknowledgment for messages informs further downstream nodes that the path has failed.
Upon receiving a DATA packet at a Dissemination Node, the local routing table is checked for an upstream link that may be used to reach the sink. The message is then buffered in case retransmission is necessary. At this moment an acknowledge message is sent back to the sender indicating acceptance or rejection, and providing flow control and energy consumption information. The forwarding procedure at a Dissemination Node continues till the DATA message stops at the sink node.
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