IACR News item: 03 May 2012
Qiang Li, Xiangxue Li, Dong Zheng, Zheng Huang, Kefei Chen
ePrint ReportWe consider in this paper the problem of finding optimal CAS\'s for incomplete AS\'s. The paper introduces some notions including the connected-super-forbidden-family and the lower-forbidden-family for AS\'s. We show that an optimal CAS can be derived from some smaller sized BIP whose variables (constraints, resp.) are based on the connected-super-forbidden-family (lower-forbidden-family, resp.) of the given AS. The paper further builds the close relationship between the problem of finding optimal CAS\'s and the set covering problem (SCP). We prove that the problem of finding a CAS with minimum cardinality of the primitive share set (or minimum average information rate) is equivalent to the SCP, and thus is NP-hard. Other contributions of the paper include: 1) two types of AS\'s are recognized so that we can construct the corresponding optimal CAS\'s directly; and 2) a greedy algorithm is proposed to find CAS\'s with smaller worst information rate.
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