Principal partitions and generators
نویسندگان
چکیده
منابع مشابه
Theory of Principal Partitions Revisited
The theory of principal partitions of discrete systems such as graphs, matrices, matroids, and submodular systems has been developed since 1968. In the early stage of the developments during 1968–75 the principal partition was considered as a decomposition of a discrete system into its components together with a partially ordered structure of the set of the components. It then turned out that s...
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A handful of recent cryptographic proposals rely on the conjectured hardness of the following problem in the ring of integers of a cyclotomic number field: given a basis of a principal ideal that is guaranteed to have a “rather short” generator, find such a generator. Recently, Bernstein and Campbell-Groves-Shepherd sketched potential attacks against this problem; most notably, the latter autho...
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Article history: Received 28 April 2014 Received in revised form 14 October 2014 Accepted 14 October 2014 Available online 31 October 2014 MSC: 54D20
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A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1967
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1967-11727-0