Page 2 Lecture Notes in Computer Science 2865 Edited by G. Goos ...

IDEA: An Iterative-Deepening Algorithm for Energy-Efficient Querying 205query may terminate before reaching the maximum depth. Let R be the IDEArule (the iterative depths) which would be used for evaluation. The rules aredefined as a set of values, where the i th value, represents the number of hopsa message is forwarded in the i th iteration (this is for 1 < i < N − 1 , for aN-item set, since the last value if the inter-iteration interval) or is halted. Let usassume d to be the item of the IDEA rule set i.e. we need to go d hops duringthe flooding approach.So the energy consumption equation (1) would change to accommodate theIDEA algorithm. It would be a sum of the energy consumed to flood the query ton hops and receiving response messages from nodes at n hops. If the query endsbefore reaching nodes which are n hops away, then it will not be sent to nodesthat are n hops away nor receive results from nodes which ar n hops away. Thiscondition can be mathematically represented as a constant A, which is multipliedto the naive energy consumption relation achieved above in eqn (1).A = 1 , if n is a rule in the IDEA-rule of iterationsand query Q does not end at nodes n hops away= 0 , otherwiseAnother important factor is the overhead caused by sending the continuemessages. continue messages are sent to nodes n hops away if:(a) depth k is in the IDEA-rule(b) query is not satisfied within depth k before expiration(c) depth k < D (max depth i.e. highest value of IDEA-rule elements)5.3 Energy Model for T-IDEAEnergy consumption equation for token-based iterative deepening is similar toequation (1), for a classical flooding approach. The only change that is incorporatedis the heuristic to decide whether a node would participate in the searchoperation in the ad hoc network, based on local decisions.6 Results6.1 Average Aggregate Energy ConsumptionFigure 1 shows the cost of each rule-item, for differnt values of inter-iterationinterval, T, in terms of average aggregate energy consumption. Along the x-axis,we vary the rule, d i.e. number of hops. Immediately obvious in these figures arethe cost savings. IDEA-Rule R 1 at T = 8 units uses just about 19% of theaggregate bandwidth per query used by classical flooding, IDEA-Rule R 7 , andjust 41% of the aggregate processing cost per query.To understand how such enormous savings are possible, we must understandthe tradeoffs between the different rules and inter-iteration interval, T. Let usfocus on energy consumption per query message, in Figure 1. First, notice that