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Abstract: By researching on the node scheduling problem of m-covered and connected sensor networks, a new concept of two-hops-cluster is proposed in this paper, and based on it, a new distributed node scheduling algorithm THCNS for allocating all nodes in the sensor network into k(k ⩽m) different groups {0, 1, ..., k −1} is designed, without requiring location information. Our algorithm guarantees that each group to be connected and maintains the coverage ratio with high possibility. Theoretical analysis and simulation results show that it has better performance than previous randomized scheduling scheme, and can prolong the lifetime of the sensor network effectively.

Super-simple designs are useful in constructing codes and designs such as superimposed codes and perfect hash families. In this article, we investigate the existence of a super-simple (ν, 5, 5) balanced incomplete block design and show that such a design exists if and only if ν ≡ 1 (mod4) and ν ≥ 17 except possibly when ν = 21. Applications of the results to optical orthogonal codes are also mentioned.Super-simple designs are useful in constructing codes and designs such as superimposed codes and perfect hash families. In this article, we investigate the existence of a super-simple (ν, 5, 5) balanced incomplete block design and show that such a design exists if and only if ν ≡ 1 (mod4) and ν ≥ 17 except possibly when ν = 21. Applications of the results to optical orthogonal codes are also mentioned.

A holey Schröder design of type h1n1h2n2… hknk(HSD(h1n1h2n2… hknk)) is equivalent to a frame idempotent Schröder quasigroup (FISQ(h1n1h2n2… hknk)) of order n with nimissing subquasigroups (holes) of order hi, (1 ⩽ i⩽ k), which are disjoint and spanning, that is, Σ1 ⩽ i⩽ knihi= n. In this paper, it is shown that an HSD(hn) exists if and only if h2n(n− 1) 0 (mod 4) with expceptions (h, n) ϵ{{(1,5),(1,9),(2,4)}} and the possible exception of (h, n) = (6,4).

A holey Schröder design of type $h^{n_{1}}_{1}h^{n_{2}}_{2} \cdots h^{n_{k}}_{k}$ $[HSD(h^{n_{1}}_{1}h^{n_{2}}_{2} \cdots h^{n_{k}}_{k})]$ is equivalent to a frame idempotent Schröder quasigroup $[FISQ(h^{n_{1}}_{1}h^{n_{2}}_{2} \cdots h^{n_{k}}_{k})] of order m with ni missing subquasigroups (holes) of order hi, 1 ≤ i ≤ k, which are disjoint and spanning, that is, ∑1≤i≤knihi = m. In this article, we first consider the existence of HSD(2ⁿu¹) for 1 ≤ u ≤ 4 and show that these HSDs exist if and only if n ≥ u + 1 with the exception of (n, u) ∈ {(2, 1), (3, 1), (3, 2)}. Then we investigate the existence of HSD(2ⁿu¹) for general u and prove that there exists an HSD(2ⁿu¹) for u ≥ 16 and n ≥ [5u/4] + 14. © 1998 John Wiley & Sons, Inc. J Combin Designs 6:131–150, 1998