Related papers: Network Coding for $3$s$/n$t Sum-Networks
We are interested in the following problem we call global sum. Each processor starts with a single real value. At each time step, every directed edge in the graph can simultaneously be used to transmit a single (bounded) number between the…
We investigate linear network coding in the context of robust function computation, where a sink node is tasked with computing a target function of messages generated at multiple source nodes. In a previous work, a new distance measure was…
The 3-Satisfiability Problem (3-SAT) is a demanding combinatorial problem, of central importance among the non-deterministic polynomial (NP) complete problems, with applications in circuit design, artificial intelligence and logistics. Even…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
Consensus is a common method for computing a function of the data distributed among the nodes of a network. Of particular interest is distributed average consensus, whereby the nodes iteratively compute the sample average of the data stored…
Sum-rank-metric codes have wide applications in universal error correction, multishot network coding, space-time coding and the construction of partial-MDS codes for repair in distributed storage. Fundamental properties of sum-rank-metric…
We consider the source-channel separation architecture for lossy source coding in communication networks. It is shown that the separation approach is optimal in two general scenarios, and is approximately optimal in a third scenario. The…
We consider the sampling problem from a composite distribution whose potential (negative log density) is $\sum_{i=1}^n f_i(x_i)+\sum_{j=1}^m g_j(y_j)+\sum_{i=1}^n\sum_{j=1}^m\frac{\sigma_{ij}}{2\eta} \Vert x_i-y_j \Vert^2_2$ where each of…
A fundamental problem in mathematics and network analysis is to find conditions under which a graph can be partitioned into smaller pieces. The most important tool for this partitioning is the Fiedler vector or discrete Cheeger inequality.…
One of the main theoretical motivations for the emerging area of network coding is the achievability of the max-flow/min-cut rate for single source multicast. This can exceed the rate achievable with routing alone, and is achievable with…
A single-source network is said to be \textit{memory-free} if all of the internal nodes (those except the source and the sinks) do not employ memory but merely send linear combinations of the incoming symbols (received at their incoming…
It is known for many algorithmic problems that if a tree decomposition of width $t$ is given in the input, then the problem can be solved with exponential dependence on $t$. A line of research by Lokshtanov, Marx, and Saurabh [SODA 2011]…
It is well known that the P3P problem could have 1, 2, 3 and at most 4 positive solutions under different configurations among its 3 control points and the position of the optical center. Since in any real applications, the knowledge on the…
For each integer $m \geq 2$, a network is constructed which is solvable over an alphabet of size $m$ but is not solvable over any smaller alphabets. If $m$ is composite, then the network has no vector linear solution over any $R$-module…
Let $n, s$ be positive integers such that $n$ is sufficiently large and $s\le n/3$. Suppose $H$ is a 3-uniform hypergraph of order $n$. If $H$ contains no isolated vertex and $deg(u)+ deg(v) > 2(s-1)(n-1)$ for any two vertices $u$ and $v$…
We investigate joint network and channel coding schemes for networks when relay nodes are not capable of performing channel coding operations. Rather, channel encoding is performed at the source node while channel decoding is done only at…
Following a suggestion of W.M. Schmidt and L. Summerer, we construct a proper $3$-system $(P_{1},P_{2},P_{3})$ with the property $\overline{\varphi}_{3}=1$. In fact, our method generalizes to provide $n$-systems with…
We abstract the essential aspects of network-error detecting and correcting codes to arrive at the definitions of matroidal error detecting networks and matroidal error correcting networks. An acyclic network (with arbitrary sink demands)…
We consider a simple multiple access network in which a destination node receives information from multiple sources via a set of relay nodes. Each relay node has access to a subset of the sources, and is connected to the destination by a…
We consider a network of two nodes separated by a noisy channel, in which the source and its reconstruction have to be strongly coordinated, while simultaneously satisfying the strong secrecy condition with respect to an outside observer of…