Related papers: On the k-pairs problem
One major open problem in network coding is to characterize the capacity region of a general multi-source multi-demand network. There are some existing computational tools for bounding the capacity of general networks, but their…
We study frequency allocation in wireless networks. A wireless network is modeled by an undirected graph, with vertices corresponding to cells. In each vertex we have a certain number of requests, and each of those requests must be assigned…
The capacity of a graph is defined as the rate of exponential growth of independent sets in the strong powers of the graph. In the strong power an edge connects two sequences if at each position their letters are equal or adjacent. We…
We study the $k$-edge connectivity problem on undirected graphs in the distributed sketching model, where we have $n$ nodes and a referee. Each node sends a single message to the referee based on its 1-hop neighborhood in the graph, and the…
In the k-partition problem (k-PP), one is given an edge-weighted undirected graph, and one must partition the node set into at most k subsets, in order to minimise (or maximise) the total weight of the edges that have their end-nodes in the…
In this paper, we study the wireline two-unicast-Z communication network over directed acyclic graphs. The two-unicast-Z network is a two-unicast network where the destination intending to decode the second message has apriori side…
Both the combinatorial and the circuit diameters of polyhedra are of interest to the theory of linear programming for their intimate connection to a best-case performance of linear programming algorithms. We study the diameters of dual…
We study multiport networks, common in electrical engineering. They have boundary conditions different from electrical networks: the boundary vertices are split into pairs and the sum of the incoming currents is set to be zero in each pair.…
We study the statistics of growing networks in which each link carries a weight (k_i k_j)^theta, where k_i and k_j are the node degrees at the endpoints of link ij. Network growth is governed by preferential attachment in which a…
Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…
Network Coding encourages information coding across a communication network. While the necessity, benefit and complexity of network coding are sensitive to the underlying graph structure of a network, existing theory on network coding often…
Network coding theory studies the transmission of information in networks whose vertices may perform nontrivial encoding and decoding operations on data as it passes through the network. The main approach to deciding the feasibility of…
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 study the prime pair counting functions $\pi_{2k}(x),$ and their averages over $2k.$ We show that good results can be achieved with relatively little effort by considering averages. We prove an asymptotic relation for longer averages of…
This paper investigates the problem of single-source multicasting over a communication network in the presence of restricted adversaries. When the adversary is constrained to operate only on a prescribed subset of edges, classical cut-set…
This paper focuses on a particular transmission scheme called local network coding, which has been reported to provide significant performance gains in practical wireless networks. The performance of this scheme strongly depends on the…
We consider two problems for a directed graph $G$, which we show to be closely related. The first one is to find $k$ edge-disjoint forests in $G$ of maximal size such that the indegree of each vertex in these forests is at most $k$. We…
The capacity of line networks with buffer size constraints is an open, but practically important problem. In this paper, the upper bound on the achievable rate of a class of codes, called batched codes, is studied for line networks. Batched…
We consider a scenario of broadcasting information over a network of nodes connected by noiseless communication links. A source node in the network has $k$ data packets to broadcast, and it suffices that a large fraction of the network…
Random linear network code has to sacrifice part of bandwidth to transfer the coding vectors, thus a head of size k log|T| is appended to each packet. We present a distributed random network coding approach based on the Chinese remainder…