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The authors present heterogeneous quorum-based asynchronous wake-up scheduling schemes for wireless sensor networks. The schemes can ensure that two nodes that adopt different quorum systems as their wake-up schedules can hear each other at least once in bounded time intervals. They propose two such schemes: cyclic quorum system pair (cqs-pair) and grid quorum system pair (gqs-pair). The cqs-pair which contains two cyclic quorum systems provides an optimal solution in terms of energy saving ratio for asynchronous wake-up scheduling. To quickly assemble a cqs-pair, they present a fast construction scheme which is based on the multiplier theorem and the (N; k;M; l)-difference pair defined by one.
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