Mobile Agent-Based Anomaly Detection and Verification System for Smart Home Sensor Networks by Muhammad Usman Vallipuram Muthukkumarasamy Xin-Wen Wu & Surraya Khanum

Author:Muhammad Usman, Vallipuram Muthukkumarasamy, Xin-Wen Wu & Surraya Khanum
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

Theorem 3.2

The time complexity for (i) The procedure for the collection of the values of features by is O(l); (ii) the procedure of abnormality identification on is U; (iii) the procedure of on-the-spot confirmation of is O(m); (iv) the procedure of update of status on is constant time V ; and (v) the procedure of update of status on BS is constant time W.

Proof

(i). Time complexity for procedure of collection of features is primarily dependent on = ; here = is calculated on after obtaining values from . Let takes l time to accumulate values of from its proximity and save them. The mote consumes , a constant time, to communicate values to . Taking the case of upper bound, the features collection procedure has O(l) time complexity.

(ii). The takes constant time to get the features from , time to check the condition , that is, received within the allocated timeslot, and time to perform the abnormality identification, . The consumes time to aggregate the sensor reading, time to check the trust value consumes, time to decrement the trust value, time for the abnormality confirmation agent dispatch to ; here is antagonist in such situations. The consumes time to transmit abnormality alarm, , to the BS mote. Thus, considering = , the algorithm for the abnormality identification procedure runs in a constant time U.

(iii). The mote receives AA and transmits on-the-spot confirmation result to in to times. The mote takes time to add a watermark in on-the-spot confirmation result. The mote takes m time to carry out the operation of comparison among the values of and . Thus, by taking the upper limit on time consumed by the procedure of comparison, the complexity of on-the-spot confirmation procedure is O(m).

(iv). The takes constant time to check confirmation result within the allocated timeslot values. It takes constant time to remove the watermark from the received result, to check the confirmation result, to check trust value, to decrement the trust value, and to transmit an abnormality alarm to BS. Thus, considering V = , the algorithm for the status update procedure on the runs in a constant time V.

(v). The BS mote consumes constant time to receive an abnormality alarm, or , from the . Similarly, the BS mote consumes time to store the received aggregated data, . Thus, considering W = + , the algorithm for the status update procedure on the BS mote runs in a constant time W.

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