The vector partition problem concerns the partitioning of a set A of n vectors in d-space into p parts so as to maximize an objective function c which is convex on the sum of vectors in each part. Here all parameters d, p, n are considered variables. In this paper, we study the adjacency of vertices in the associated partition polytopes. Using our adjacency characterization for these polytopes,...

123, 12|3, 13|2, 23|1, 1|2|3. The blocks are unordered, so 2|13 is the same partition as 13|2 and 2|31. A partition B is a sub-partition of B∗ if each block of B is a subset of some block of B∗ or, equivalently, if Bij = 1 implies B∗ ij = 1. This relationship is a partial order denoted by B ≤ B∗, which can be interpreted as B ⊂ B∗ if each partition is regarded as a subset of [n]2. The partition...

At present, due to the fact that large-scale distributed photovoltaics can access distribution networks and there is a mismatch between load demand photovoltaic output time, it difficult for traditional planning meet partition-based control of high permeability grid-connected operations. As solution this problem, paper proposes method storage partitions. First all, partitioning electrical dista...

For positive integers and , consider a multiset of nonempty subsets such that there is unique partition these into partitions . We study the maximum possible size multiset. focus on regime show When for any this lower bound simplifies to we matching upper optimal up factor also compute exactly when

The upper chromatic number (H) of a hypergraphH= (X,E) is the maximum number k for which there exists a partition of X into non-empty subsets X=X1 ∪X2 ∪ · · · ∪Xk such that for each edge at least two vertices lie in one of the partite sets. We prove that for every n 3 there exists a 3-uniform hypergraph with n vertices, upper chromatic number 2 and n(n− 2)/3 edges which implies that a correspon...

It is necessary to compute the execution time upper bound of embedded hard real-time program under the worst condition in embedded system design, which decides how hardware and software to partition and how to schedule process. Modern microprocessors which use cache memory system and instruction pre-fetching increase the difficulty to compute the upper bound accurately. A new estimation method ...

We consider the problem of clustering a set of items into subsets whose sizes are bounded from above and below. We formulate the problem as a graph partitioning problem and propose an integer programming model for solving it. This formulation generalizes several well-known graph partitioning problems from the literature like the clique partitioning problem, the equi-partition problem and the k-...

In this note, we define the concepts of admissible relation and admissible partition for an arbitrary BL-general fuzzy automaton.In particular, a connection between the admissible partition and the quotient BL-general fuzzy automaton is presented.It is shown that if we use the maximal admissible partition, then we obtain a quotient BL-general fuzzy automaton and this quotient is minimal. Finall...

In the fractional graph colouring problem, the task is to schedule the activities of the nodes so that each node is active for 1 time unit in total, and at each point of time the set of active nodes forms an independent set. We show that for any α > 1 there exists a deterministic distributed algorithm that finds a fractional graph colouring of length at most α(∆ + 1) in any graph in one synchro...