Related papers: Multicut Lower Bounds via Network Coding
We give an information flow interpretation for multicasting using network coding. This generalizes the fluid model used to represent flows to a single receiver. Using the generalized model, we present a decentralized algorithm to minimize…
How many links can be cut before a network is bisected? What is the maximal bandwidth that can be pushed between two nodes of a network? These questions are closely related to network resilience, path choice for multipath routing or…
In the All-Reduce problem, each one of the K nodes holds an input and wishes to compute the sum of all K inputs through a communication network where each pair of nodes is connected by a parallel link with arbitrary bandwidth. The…
In any communication network, the maximum number of link-disjoint paths between any pair of communicating nodes, S and T, is limited by the S-T minimum link-cut. Multipath routing protocols have been proposed in the literature to make use…
Random linear network coding is a particularly decentralized approach to the multicast problem. Use of random network codes introduces a non-zero probability however that some sinks will not be able to successfully decode the required…
Based upon the idea that network functionality is impaired if two nodes in a network are sufficiently separated in terms of a given metric, we introduce two combinatorial \emph{pseudocut} problems generalizing the classical min-cut and…
In a single hop broadcast packet erasure network, we demonstrate that it is possible to provide multirate packet delivery outside of what is given by the network min-cut. This is achieved by using a deterministic non-block-based network…
The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…
We study upper bounds on the sum-rate of multiple-unicasts. We approximate the Generalized Network Sharing Bound (GNS cut) of the multiple-unicasts network coding problem with $k$ independent sources. Our approximation algorithm runs in…
Given an edge-weighted graph $G$ on $n$ nodes, the NP-hard Max-Cut problem asks for a node bipartition such that the sum of edge weights joining the different partitions is maximized. We propose a fixed-parameter tractable algorithm…
Consider the following "local" cut-detection problem in a directed graph: We are given a starting vertex $s$ and need to detect whether there is a cut with at most $k$ edges crossing the cut such that the side of the cut containing $s$ has…
The problem of network coding with multicast of a single source to multisink has first been studied by Ahlswede, Cai, Li and Yeung in 2000, in which they have established the celebrated max-flow mini-cut theorem on non-physical information…
An instance of the graph-constrained max-cut (GCMC) problem consists of (i) an undirected graph G and (ii) edge-weights on a complete undirected graph on the same vertex set. The objective is to find a subset of vertices satisfying some…
We investigate to what extent the degree sequence of a directed network constrains the number of driver nodes. We develop a pair of algorithms that take a directed degree sequence as input and aim to output a network with the maximum or…
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…
The Edge Multicut problem is a classical cut problem where given an undirected graph $G$, a set of pairs of vertices $\mathcal{P}$, and a budget $k$, the goal is to determine if there is a set $S$ of at most $k$ edges such that for each…
We consider the multiple unicast problem under network coding over directed acyclic networks when there are two source-terminal pairs, $s_1-t_1$ and $s_2-t_2$. Current characterizations of the multiple unicast capacity region in this…
In this paper, we study a \emph{multicut-mimicking network} for a hypergraph over terminals $T$ with a parameter $c$. It is a hypergraph preserving the minimum multicut values of any set of pairs over $T$ where the value is at most $c$.…
This work considers the multiple-access multicast error-correction scenario over a packetized network with $z$ malicious edge adversaries. The network has min-cut $m$ and packets of length $\ell$, and each sink demands all information from…
We study network coding gaps for the problem of makespan minimization of multiple unicasts. In this problem distinct packets at different nodes in a network need to be delivered to a destination specific to each packet, as fast as possible.…