Ternary Schedules for Energy-Limited Sensor Networks

Medium access control for multihop wireless sensor networks (WSNs) must be energy efficient because the battery-operated nodes are not practical to recharge. We give constructions for ternary schedules in which each node is in one of three states: transmitting, receiving, or asleep. For each hop (v
_i
, v
_j
), communication is effective only when v
_i
is transmitting, v
_j
is receiving, and no other node in proximity of v
_j
is also transmitting. Since sensor nodes are prone to failure, the schedules should be independent of the detailed topology while supporting spatial reuse. We use arc-decompositions of the complete lambda-fold directed graph Koarr
_n
into directed complete bipartite subgraphs Koarr
_a,b
as a model for ternary scheduling in WSNs. We associate the vertices of Koarr
_n
with the nodes of the WSN, and occurrences of Koarr
_a,b
s (blocks) in the decomposition with time slots in the schedule. A block with out-vertices A and in-vertices B corresponds to a slot in which the a nodes in A are transmitting, the b in B are receiving, and all others are asleep. Such a decomposition of lambdaKoarr
_n
guarantees that every ordered pair of nodes in the WSN can communicate in lambda time slots.