We study fractional scheduling problems in sensor networks, in particular, sleep scheduling (generalisation of fractional domatic partition) and activity scheduling (generalisation of fractional graph colouring). The problems are hard to solve in general even in a centralised setting; however, we show that there are practically relevant families of graphs where these problems admit a local dist...

Given a family of subsets of an n-element universe, the kcover problem asks whether there are k sets in the family whose union contains the universe; in the k-packing problem the sets are required to be pairwise disjoint and their union contained in the universe. When the size of the family is exponential in n, the fastest known algorithms for these problems use inclusion–exclusion and fast zet...

In this paper, we show detailed analysis and performance evaluation of the Dynamic Hybrid GRACE Hash Join Method (DHGH Method) when the tuple distribution in buckets is unbalanced. The conventional Hash Join Methods specify the tuple distribution in buckets statically. However it may differ from estimation since join operations are applied with selection operations. When the tuple distribution ...

Let k be a positive integer. A subset S of V (G) in a graph G is a k-tuple total dominating set of G if every vertex of G has at least k neighbors in S. The k-tuple total domination number γ×k,t(G) of G is the minimum cardinality of a k-tuple total dominating set of G. In this paper for a given graph G with minimum degree at least k, we find some sharp lower and upper bounds on the k-tuple tota...

The n-tuple of Laplacian characteristic values of a graph is majorized by the conjugate sequence of its degrees. Using that result we find a collection of general inequalities for a number of Laplacian indices expressed in terms of the conjugate degrees, and then with a maximality argument, we find tight general bounds expressed in terms of the size of the vertex set n and the average degree dG...

The inflated graph GI of a graph G with n(G) vertices is obtained from G by replacing every vertex of degree d of G by a clique, which is isomorph to the complete graph Kd, and each edge (xi, xj) of G is replaced by an edge (u, v) in such a way that u ∈ Xi, v ∈ Xj , and two different edges of G are replaced by non-adjacent edges of GI . For integer k ≥ 1, the k-tuple total domination number γ ×...