Decentralized Boundary Detection without Location
Information in Wireless Sensor Networks
Wei-Cheng Chu
Institute of Computer and Communication Engineering Department of Electrical Engineering
National Cheng Kung University Tainan, Taiwan
Email: 491191291@s91.tku.edu.tw
Kuo-Feng Ssu
Institute of Computer and Communication Engineering Department of Electrical Engineering
National Cheng Kung University Tainan, Taiwan
Email: ssu@ee.ncku.edu.tw
Abstract—In wireless sensor networks (WSNs) deployed in an outdoor environment, obstacles may occur as a result of a non-uniform distribution of the sensor nodes or the presence of barriers. These obstacles result in a degradation of the network performance, so obstacle identification is a major concern in most WSN applications. This paper develops a Decentralized Boundary Detection (DBD) algorithm for identifying sensor nodes near a hole or obstacle in the WSN. The algorithm does not require any knowledge of the node locations or distances between two nodes. The detection capability is provided even in networks where the sensor nodes have a non-unit disk communication range.
I. INTRODUCTION
Wireless sensor networks (WSNs) have a wide range of po-tential applications, such as environment monitoring, military, smart house, and so forth. WSNs are generally deployed in an outdoor environment, and thus their performance is affected by the presence of obstacles within the sensing field. In practice, these obstacles arise for various reasons. For example, the initial random deployment of the sensor nodes cannot cover the sensing field completely. In addition, the sensor nodes are generally battery-operated and therefore have a limited service life. Once the nodes have consumed all their energy, the sensing and communication functionality in the corresponding region is degraded. Furthermore, the environment may contain physical obstacles such as mountains or buildings, which pre-vent the propagation of the communication signals generated by the sensors. Finally, even in the absence of such obstacles, the sensor signals may still be adversely affected by animus signal interference. In general, a geographic region without the functionality of sensing or communication is treated as an obstacle that can significantly drop the performance of the communication protocols. Consequently, detecting the pres-ence of obstacles in the sensing field is an essential task in improving the performance of most WSN applications [21], [4].
Various researchers [11], [15], [2], [3] proposed stereovision systems based on image-processing algorithms for obstacle detection. They demonstrated that such systems enable a robot to navigate a path between two pre-determined end points while successfully avoiding any obstacles encountered along the way. However, these schemes are all intended for mobile
robots and are therefore impractical for large-scale WSNs con-taining hundreds or thousands of sensor nodes. The literature contains many location-based algorithms for detecting physical obstacles and communication holes in WSNs [6], [18], [20], [14]. These algorithms are based on the assumption that each sensor is aware of its own location with high accuracy, so the obstacles can be detected using a coordinate system computing approach executed by each sensor node and its neighbors. This assumption is not realistic in a real world. Neither GPS nor other localization mechanisms can provide sufficiently accurate sensor location. Consequently, the use of location-free algorithms has become increasingly common in recent years [10], [7], [8], [9], [19], [17], [13], [16], [12], [5]. The algorithms suffer high communication overhead, which is not suitable for the dynamic hole detection (e.g., a new hole appears when a node exhausts its energy or leaves the network field).
Accordingly, this paper presents an efficient mechanism, Decentralized Boundary Detection (DBD), to accomplish ob-stacle detection in WSNs without the need for any loca-tion informaloca-tion or any knowledge of the distance among the sensor nodes. The proposed scheme utilizes three-hop neighboring node information and is implemented using a distributed approach. Therefore, the control overhead can be smaller compared to the topology-based boundary detection method. Additionally, DBD does not enforce the Unit Disk Graph (UDG) constraint.
II. RELATEDWORK
Fekete et al. [7] counted the number of the shortest paths between all pairs of k-hop neighbors passing through a sensor node and defined the node as a boundary node (i.e., a node adjacent to an obstacle) if the number was less than a certain pre-determined threshold. Calculating an appropriate threshold for a particular WSN is actually non-trivial since the node density is not a constant throughout the sensing field, but varies from one region to another. An improved research proposed by Kr¨oller et al. [12] introduced the “flower” structure to recognize the inner and outer boundaries. Each inner or outer boundary is consisted of several segments of flower boundaries. The flower combination eliminates the redundant 2012 IEEE Wireless Communications and Networking Conference: Mobile and Wireless Networks
segments of flower boundaries, where the remaining segments of flower boundaries include the inner and outer boundaries. Saukh et al. [17] also applied the flower structure to recognize the boundaries. The flower structures are developed for both unit disk graph and quasi unit disk graph [17], which is more realistic. The boundary nodes determined in research [17] are guaranteed not to be inner nodes that must be inside the network.
Various researchers have proposed topology-based methods for identifying boundary nodes using a repetitive flooding mechanism [8], [9], [19]. Funke et al. [9] presented a Topo-logical Hole Detection (THD) scheme for identifying the breakpoints of the contours which are 3-hop away from a seed [9]. A seed is a node which belongs to the maximal independent set of all nodes in the network. If a contour cannot form a cycle, the breakpoints of the contour play the inner or outer boundary node roles. THD also uses a pruning rule to decrease the number of boundary nodes in order to reduce the computational complexity of the boundary detection process. Wang et al. [19] developed a special structure of the shortest path trees to detect nodes on the boundaries and connect them into boundary cycles. However, the control overhead incurred in performing the flooding procedure to detect the boundary nodes increases significantly with a large number of holes. To reduce the control overhead, Li et al. [13] proposed a 3MeSH algorithm [13] to accomplish hole detection based upon two-hop neighboring information only. The 3MeSH algorithm considers only Voronoi neighbors so it may fail for non-Voronoi neighbors due to its inability to take the associated cross links into account. Reichenbach et al. [16] proposed a beacon-based approach to obstacle detection for WSNs in which the beacons were assumed to be distributed over regular grids. Adopting the assumption that the presence of obstacles resulted in a partial suppression of the sensor signals, each node nominated itself as a boundary corner node (or not) by evaluating the signals received from its neighbors.
Dong et al. [5] proposed TTG to identify any size of a hole. Simple-connectedness graph [5] is proposed to construct the cycles, which each of them contains exact one hole in the network. Minimizing a cycle length thus can identify the boundary of a hole. TTG requires to collect the k-hop neighbors’ information for each step of algorithm to construct the simple-connectedness graph, where k is larger than two. The control overhead is significantly raised if the network topology is dynamic.
III. DECENTRALIZEDBOUNDARYDETECTION
A. Network Assumptions and System Model
In DBD, it is assumed that each node is unaware of its own location but knows its three-hop neighbors by means of HELLO messages, one-hop, and two-hop node information. The network is represented as a connected graph G = (VG, EG), where VG is the node set of graph G and each
edge in EG is a two-way communication link. DBD can be
applied in the network with UDG or quasi-UDG embedding. The d-Quasi Unit Disk Graph (d-QUDG) is first discussed by
Fig. 1. The outer boundary is a hole cycle.
literature [1]. The parameter d denotes the rate of stable com-munication range to the maximum comcom-munication range. Let uv denote the Euclidean distance between nodes u and v. Assume that the maximum communication range is set as 1. A d-QUDG satisfies two conditions: (1) uv∈ EG⇒ uv ≤ 1,
and (2) uv∈ EG ⇐ uv ≤ d. Researches [12], [17] adopt d-QUDG model with d ≥ √2/2 to recognize the boundary. DBD intends to recognize the boundary without any constraint of the value of d.
B. Definition of Hole
Dong et al. [5] indicates that hole boundaries have two properties: continuity and consistency. Continuity means that all nodes in a boundary can form loop-like connection instead of being isolated. Consistency means that a boundary encircles holes in any embedding. A graph embedding is a particular drawing of a graph. The boundaries include outer boundaries and inner boundaries. This paper gives the definition of hole which contains above two properties.
Definition 1. A cycle divides the plane into two parts: the
outside face and the inside face. If the length of a cycle is larger than three and it cannot be decomposed into several cycles with the smaller length, the cycle is denoted as a hole cycle. A hole is an inside face formed by the hole cycle in graph G.
Notice that the outer boundary (network boundary) is also a hole cycle in a specific graph embedding. For example, in Fig. 1, the outer boundary abcdefgh of left illustration is a hole cycle abcdefgh in right illustration with varying embedding.
C. DBD
Since each node maintains its 3-hop neighbors’ informa-tion, a “2-hop-neighbor graph” as following definition is constructed by each node.
Definition 2. Let Nk
s be the k-hop neighbor set of node s (Ns0
equals node s). Let Eij
s denote the edge set where each edge
is consisted of two endpoints in Ni
s and Nsj, respectively. A
2-hop-neighbor graph of node s is denoted as G
s = (Ns1∪
Ns2∪ s, Es01∪ Es11∪ Es12∪ Es22). The cycle which is inside graph G
s can be detected by
node s. It indicates that node s is aware of the hole formed by such cycle.
Fig. 2. An example of contour lines.
Rule 1. If there exists a hole in graph G
s, node s is a boundary
node.
Rule 1 is designed to detect the hole within graph G s by
node s. To against the hole which is not totally included in 2-hop-neighbor graph, DBD develops another detection rule, which is based on the contour structure [8].
Consider a point s in the planar field as shown in Fig. 2. Draw the circles centered at point s with radiuses 1, 2, 3,.... These circles form the contour lines. Fig. 2 shows that some contour lines encounter the network boundary or an obstacle (the gray area), and they fail to form complete circles. Let point s be a node in the network. If a broken contour line is detected by node s, it is aware that the contour line has encountered the network boundary or an obstacle. However, node s is unaware of its location and the contour lines are virtual lines that they cannot really “encounter” the network boundary or an obstacle. Therefore, the contour line is replaced by Nk
s and one-hop distance is regarded as a unit distance.
Definition 3. The k-contour of node s is a graph Ck s =
(Nk
s, Eskk), where k > 1.
As the contour structure is defined, the next concern is determining whether a contour is broken or not. Arbitrarily select a node t∈ Nk
s. Let node t do the flooding method in
graph Ck
s, and tree Ts,tk rooted at node t is then constructed.
The height of tree Tk
s,t is denoted as H(Ts,tk ), and the node
set in tree Tk
s,t with depth l is represented as Dk,ls,t. For any
node m ∈ Dk,H(Ts,tk)/2
s,t , the broken contour is defined as
below.
Definition 4. Let E(S) ⊂ EG denote the link set in node
set S. Contour Ck
s is broken if any one of following conditions
holds:
1) All heights of trees constructed by flooding method in graph Ck
s are smaller than or equal to three.
2) For any tree Tk
s,t, the corresponding (U, E(U)) is a
disconnected graph, where U = Nk
s \ ((Nm1 ∪ Nm2 ∪
m) ∩ Dk,H(T
k s,t)/2
s,t ).
Figs. 3(a)∼(c) shows an example of the detection of the bro-ken contour of node s. Node s constructs tree Tk
s,t(Fig. 3(b)) in
Fig. 3. An example of a broken contour of node s. (a) Graph Ck s. (b)
TreeTk
s,t. (c) Graph (U, E(U)) of definition 4. (d) Tree Ts,mk , the white
squares are leaf nodes.
graph Ck
s (Fig. 3(a)). Since contour Csk is broken, the graph
in Fig. 3(c) is disconnected. As each node maintains its 2-hop-neighbor graph, it constructs its2-contour to execute the following rule.
Rule 2. If contour C2
s is broken, node s is a boundary node.
A node is a boundary node if it matches any one of two rules. The next section shows the proof of the correctness of two rules.
IV. PROOF OFCORRECTNESS
Lemma 1. A hole cycle has two properties: continuity and consistency.
Proof. Since hole cycle is a cycle, the continuity property
holds. On the other hand, a cycle, represented by sets VG
and EG, does not change its structure with any embedding of
graph G. Therefore, the consistency property also holds. 2
Theorem 1. Let the nodes of hole cycle be denoted as “tightly
boundary nodes”. All tightly boundary nodes can be identified as boundary nodes by DBD.
Proof. Let node s be any one of tightly boundary nodes.
For the hole cycle with length smaller than 6, it belongs to graph G
s that can be detected by node s. Node s is identified
as a boundary node by Rule 1.
For the hole cycle with length larger than 5, a pair of tightly boundary nodes, say a and b, belong to set N2
s. Two cases
are considered. First, if no path can be constructed between nodes a and b in contour C2
s, contour Cs2 is a disconnected
graph and becomes a broken contour. Second, if there exists a path between nodes a and b in contour C2
s, tree Ts,a2 contains
graph C2
s cannot enclose the hole. Further, node b is a leaf
node in tree T2
s,athat matches the second condition of Def. 4.
It indicates that contour C2
s is broken. Both cases indicate that
contour C2
s is broken, so node s is identified as a boundary
node by Rule 2.
Since node s can be any tightly boundary node, the theorem
is proved. 2
Theorem 2. Let other identified boundary nodes which are
not tightly boundary nodes named “coarsely boundary node”. If node s is a coarsely boundary node, there exists at least one tightly boundary node in N2
s or Ns1.
Proof. The proof is considered as two cases.
Case 1: Node s is identified by Rule 1. Graph G
s contains
a hole cycle, and all edges of the hole cycle belong to edge set E01
s ∪ Es11∪ Es12∪ E22s . There exists at least one tightly
boundary node in set N1
s or Ns2.
Case 2: Node s is identified by Rule 2. Assume that tree T2
s,t
matches the second condition of Def. 4. Let the leaf set of tree T2 s,m be L2s,m, where node m ∈ D2,H(T 2 s,t)/2 s,t . Since contour C2 s is broken, graph LG2s,m = (L2s,m, E(L2s,m)) is
disconnected and consists at least two connected components, such as an example in Fig. 3(d) with k = 2. A connected component of graph LG2
s,m is one of the maximal connected
subgraphs of graph LG2
s,m.
Assume all nodes in L2
s,m are not tightly boundary nodes.
For each node n ∈ L2
s,m, Nn1 can form a polygon which
encloses node n, where each edge of the polygon belongs to E11
n . Therefore, for each component A ⊂ LG2s,m, there
exists a polygon P , which is formed by the neighbors of node set VA, enclosing A. Set VP can be classified into three types:
subset of N1
s, subset of Ns2, and subset of Ns3. As an example
shown in Fig. 3(d) with k= 2, the triangles denote the nodes which belong to N1
s ∩ VP, the black squares are nodes which
belong to N2
s∩VP, and the white diamonds belong to Ns3∩VP.
The nodes which belong to N2
s ∩ VP form two components.
The nodes of one component form a parent set of set VA in tree T2
s,m, and the nodes of the other component form a
child set of set VA in tree T2
s,m. Since set VA has a child
set, VA is not a leaf set of tree Ts,m2 , which contradicts to
the assumption. Therefore, there exists at least one tightly boundary node in L2
s,m. Since set L2s,m ⊂ Ns2, there exists
at least one tightly boundary node in N2
s. 2
Theorem 3. The boundaries identified by DBD contain both
continuity and consistency properties.
Proof. According to Theorems 1 and 2, all boundaries
(outer and inner boundaries) can be found by DBD, and the boundaries identified by DBD are also outer or inner boundaries. By Lemma 1, the boundaries identified by DBD contain both continuity and consistency properties. 2
V. PERFORMANCEEVALUATION
The detection performance of the DBD scheme is evaluated in terms of the control overhead and the boundary detection
TABLE I
CONTROLOVERHEADS OFFIVEMETHODS WITHDEGREES FROM7TO19
7 9 11 13 15 17 19 DBD 3.00 3.00 3.00 3.00 3.00 3.00 3.00 THD 20.25 23.18 33.40 42.85 49.26 55.98 62.20 THD-P 20.42 23.34 33.54 42.95 49.35 56.05 62.26 BR 7.00 7.00 7.00 7.00 7.00 7.00 7.00 TTG 654.37 588.26 522.18 456.14 390.10 324.07 258.05
Fig. 4. Boundaries detected by five methods in WSN with grid-random deplyment and 1-QUDG. (a) Node deployment. (b) DBD. (c) TTG. (d) BR. (e) THD. (f) THD-P.
with varying d-QUDGs by NS2. The size of the sensing field is 600m×600m. The maximum transmission range of each node is set as 20m. The simulations consider five different detection schemes, namely DBD, THD [9], THD-P, BR [17], and TTG [5], where THD-P denotes the THD method with the pruning rule (maximal independent set). The simulation results is the average of fifty separate experiments.
Table I compares the control overheads of five schemes in terms of the average number of packets sent per node. Each value is an average result from 1-QUDG and 0.7-QUDG environments with random deployment. Since DBD and BR require 3-hop and 7-hop neighboring information, respectively, the control overheads remain constant irrespective of the degree (the number of neighboring nodes). The control overheads of THD and THD-P vary in direct proportion to the degree since there are more nodes participating the repetitive flooding mechanism for identifying the breakpoints of contours. On the other hand, the control overhead of TTG is inverse proportional to the degree due to the less number of communication holes. TTG needs “refine inner boundary cycle” [5] for each communication hole. However, repetitive vertex deletion and edge deletion [5] cause a large amount of control overhead, so TTG is not suitable for the detection of new hole.
Fig. 5. Boundaries detected by five methods in WSN with grid-random deplyment and 0.7-QUDG. (a) Node deployment. (b) DBD. (c) TTG. (d) BR. (e) THD. (f) THD-P.
obtained by the five schemes with degree 12. DBD identifies all inner and outer boundaries in the network, no matter what the hole size and d-QUDG are. On the other hand, THD and THD-P cannot identify the boundary between two holes if the holes get too close. Further, the boundary of hole cannot be identified if the size of hole is too small (as the hole formed by the cycle with length 4 in Fig. 4). BR cannot identify the boundaries if the hole is formed by the cycle with length smaller than 14 (bases on the collection of 7-hop neighboring information). Although TTG identifies all holes in the different environments, the accuracy of the recognized hole shapes is less than that of DBD.
VI. SUMMARY
In real-world WSNs, the performance of routing or coverage protocols is commonly degraded as a result of the presence of obstacles. Thus, obstacle detection is an important concern in most WSN applications. Previous boundary detection methods are generally dependent upon each node being aware of both its own location and that of its neighbors. However, accurate location information is unavailable in most WSNs. Accordingly, this paper has developed a location-free and decentralized boundary detection (DBD) scheme which re-quires only a knowledge of the three-hop neighboring node information. The correctness proof and simulation results have shown that DBD successfully detects all boundaries in the WSN with the smaller control overhead, and can apply in dynamic networks or new hole occurrence. Moreover, it has been shown that DBD can be applied in the environment with varying d-QUDGs.
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