A perfect (t, w, v; m)-threshold scheme is a type of combinatorial design that provides a way of distributing partial information (chosen from a set of v points called shadows) to w participants, so that any t of them can easily calculate one of m possible keys, but no subset of fewer than t participants can determine any partial information regarding the key. In this paper, we give a survey of...

Let m and n be positive integers. The algorithmic search for perfect dominating sets of the rectangular grid Gm;n satisfying an initial condition S 0 de ned as an admissible subset of a side Gm;1 of Gm;n such that S \ Gm;1 = S 0 is considered. A binary decision algorithm that generates all such perfect dominating sets is presented, and some related questions and conjectures are posed, leading t...

A restricted permutation of a locally finite directed graph $ G = (V, E) is vertex \pi: V\to V for which (v, \pi(v))\in E $, any v\in $. The set such permutations, denoted by \Omega(G) with group action induced from subset isomorphisms form topological dynamical system. We focus on the particular case presented Schmidt and Strasser [18] {\mathbb Z}^d in subshift type. show correspondence betwee...

A perfect matching in a 3-uniform hypergraph on n = 3k vertices is a subset of n3 disjoint edges. We prove that if H is a 3-uniform hypergraph on n = 3k vertices such that every vertex belongs to at least ( n−1 2 ) − ( 2n/3 2 ) + 1 edges then H contains a perfect matching. We give a construction to show that this result is best possible.

In some supervised classification problems, the presence of a particular subset of features may be perfectly predictive of a data point’s class label. Discovery of these perfect-predictor feature sets can be used to explore the data and help create new features that capture dependencies among existing features. In this paper, we test the capability of genetic algorithms for finding perfect-pred...

Let X be any partially ordered set, R any commutative ring, and T = I * (X,R) the weak incidence algebra of X over R. Let Z be a finite nonempty subset of X, L(Z) = {x ∈ X : x z for some z ∈ Z}, and M = Te Z. Various chain conditions on M are investigated. The results so proved are used to construct some classes of right perfect rings that are not left perfect.

A subset S ⊆ V in a graph G = (V,E) is a [1, 2]-set if for every vertex v ∈ V \ S, 1 ≤ |N(v)∩ S| ≤ 2, that is, every vertex v ∈ V \ S is adjacent to at least one but not more than two vertices in S. In this paper we relate the concept of [1, 2]-sets to a host of other concepts in domination theory, including perfect domination, efficient domination, nearly perfect sets, 2-packings and k-depende...

In this paper, leader–follower coordination problems of a kind of heterogeneous multi-agent systems are studied by applying iterative learning control (ILC) scheme in a repeatable control environment. The heterogeneous multi-agent systems are composed of first-order and second-order dynamics in two aspects. The leader is assumed to have second-order dynamics and the trajectories of the leader a...

A perfect matching in a 4-uniform hypergraph is a subset of b4 c disjoint edges. We prove that if H is a sufficiently large 4-uniform hypergraph on n = 4k vertices such that every vertex belongs to more than ( n−1 3 ) − ( 3n/4 3 ) edges then H contains a perfect matching. This bound is tight and settles a conjecture of Hán, Person and Schacht.

Let F be a family of graphs. Two graphs G1 = (V1, E1), G2 = (V2, E2) are said to have the same F-structure if there is a bijection f : V1 → V2 such that a subset S induces a graph belonging to F in G1 if and only if its image f(S) induces a graph belonging to F in G2. We prove that graph H is perfect if and only if it has the {P3, P 3}-structure of some perfect graph G.