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...

We consider setting up sleep scheduling in sensor networks. We formulate the problem as an instance of the fractional domatic partition problem and obtain a distributed approximation algorithm by applying linear programming approximation techniques. Our algorithm is an application of the Garg-Könemann (GK) scheme that requires solving an instance of the minimum weight dominating set (MWDS) prob...

Let $kgeq 1$ be an integer, and $G=(V,E)$ be a finite and simplegraph. The closed neighborhood $N_G[e]$ of an edge $e$ in a graph$G$ is the set consisting of $e$ and all edges having a commonend-vertex with $e$. A signed Roman edge $k$-dominating function(SREkDF) on a graph $G$ is a function $f:E rightarrow{-1,1,2}$ satisfying the conditions that (i) for every edge $e$of $G$, $sum _{xin N[e]} f...