Related papers: Strong bounds and exact solutions to the minimum b…
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…
We show NP-hardness of the minimum latency scheduling (MLS) problem under the physical model of wireless networking. In this model a transmission is received successfully if the Signal to Interference-plus-Noise Ratio (SINR), is above a…
Broadcasting concerns the dissemination of a message originating at one node of a network to all other nodes. This task is accomplished by placing a series of calls over the communication lines of the network between neighboring nodes,…
Broadcast is a ubiquitous distributed computing problem that underpins many other system tasks. In static, connected networks, it was recently shown that broadcast is solvable without any node memory and only constant-size messages in…
In this paper, we propose to study on sufficient control of complex networks which is to control a sufficiently large portion of the network, where only the quantity of controllable nodes matters. To the best of our knowledge, this is the…
Highly dynamic networks rarely offer end-to-end connectivity at a given time. Yet, connectivity in these networks can be established over time and space, based on temporal analogues of multi-hop paths (also called {\em journeys}).…
Given a weighted graph $G(V,E)$ and $t \ge 1$, a subgraph $H$ is a \emph{$t$--spanner} of $G$ if the lengths of shortest paths in $G$ are preserved in $H$ up to a multiplicative factor of $t$. The \emph{subsetwise spanner} problem aims to…
We consider a standard distributed optimisation setting where $N$ machines, each holding a $d$-dimensional function $f_i$, aim to jointly minimise the sum of the functions $\sum_{i = 1}^N f_i (x)$. This problem arises naturally in…
In the literature, several different identification problems in graphs have been studied, the most widely studied such problems are the ones based on dominating sets as a tool of identification. Hereby, the objective is to separate any two…
We consider the Minimum Coverage Kernel problem: given a set $B$ of $d$-dimensional boxes, find a subset of $B$ of minimum size covering the same region as $B$. This problem is $\mathsf{NP}$-hard, but as for many $\mathsf{NP}$-hard problems…
In this paper we show that the Index Coding problem captures several important properties of the more general Network Coding problem. An instance of the Index Coding problem includes a server that holds a set of information messages…
Minimal multicast networks are fascinating and efficient combinatorial objects, where the removal of a single link makes it impossible for all receivers to obtain all messages. We study the structure of such networks, and prove some…
In this paper, we propose a distributed algorithm for the minimum dominating set problem. For some especial networks, we prove theoretically that the achieved answer by our proposed algorithm is a constant approximation factor of the exact…
We focus on the following instance of an index coding problem, where a set of receivers are required to decode multiple messages, whilst each knows one of the messages a priori. In particular, here we consider a generalized setting where…
We consider the communication complexity of finding an approximate maximum matching in a graph in a multi-party message-passing communication model. The maximum matching problem is one of the most fundamental graph combinatorial problems,…
Coding schemes with extremely low computational complexity are required for particular applications, such as wireless body area networks, in which case both very high data accuracy and very low power-consumption are required features. In…
This work discusses the source broadcasting problem, i.e. transmitting a source to many receivers via a broadcast channel. The optimal rate-distortion region for this problem is unknown. The separation approach divides the problem into two…
We consider the distributed weight balancing problem in networks of nodes that are interconnected via directed edges, each of which is able to admit a positive integer weight within a certain interval, captured by individual lower and upper…
We investigate the multiple-input multiple-output broadcast channel with statistical channel state information available at the transmitter. The so-called linear assignment operation is employed, and necessary conditions are derived for the…
In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…