Related papers: Scalar Solvability of Network Computation Problems…
For a natural number $c$, a $c$-arrangement is an arrangement of dimension $c$ subspaces satisfying the following condition: the sum of any subset of the subspaces has dimension a multiple of $c$. Matroids arising as normalized rank…
Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by…
This work addresses the $K$-user computation broadcast problem consisting of a master node, that holds all datasets and users for a general class of function demands, including linear and non-linear functions, over finite fields. The master…
Matroid theory is fundamentally connected with index coding and network coding problems. In fact, the reliance of linear index coding and network coding rates on the characteristic of a field has been demonstrated by using the two…
A scalable algorithm for solving compact banded linear systems on distributed memory architectures is presented. The proposed method factorizes the original system into two levels of memory hierarchies, and solves it using parallel cyclic…
We study the communication complexity of linear algebraic problems over finite fields in the multi-player message passing model, proving a number of tight lower bounds. Specifically, for a matrix which is distributed among a number of…
Feedforward neural networks offer a promising approach for solving differential equations. However, the reliability and accuracy of the approximation still represent delicate issues that are not fully resolved in the current literature.…
This paper establishes the rate region for a class of source coding function computation setups where sources of information are available at the nodes of a tree and where a function of these sources must be computed at the root. The rate…
Matrix representations are a powerful tool for designing efficient algorithms for combinatorial optimization problems such as matching, and linear matroid intersection and parity. In this paper, we initiate the study of matrix…
Distributed computation is a framework used to break down a complex computational task into smaller tasks and distributing them among computational nodes. Erasure correction codes have recently been introduced and have become a popular…
Lying at the interface between Network Science and Machine Learning, node embedding algorithms take a graph as input and encode its structure onto output vectors that represent nodes in an abstract geometric space, enabling various…
An important issue in neural network research is how to choose the number of nodes and layers such as to solve a classification problem. We provide new intuitions based on earlier results by An et al. (2015) by deriving an upper bound on…
Over the past years, embedding learning on networks has shown tremendous results in link prediction tasks for complex systems, with a wide range of real-life applications. Learning a representation for each node in a knowledge graph allows…
A dynamic flow network consists of a directed graph, where nodes called sources represent locations of evacuees, and nodes called sinks represent locations of evacuation facilities. Each source and each sink are given supply representing…
In a series of papers N. Ma and P. Ishwar (2011-13) considered a range of distributed source coding problems that arise in the context of iterative computation of functions, characterizing the region of achievable communication rates. We…
Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. A traditional approach is to look for codes which simultaneously maximize error tolerance and minimize storage space consumption. However, this…
In this study, we consider a class of linear matroid interdiction problems, where the feasible sets for the upper-level decision-maker (referred to as a leader) and the lower-level decision-maker (referred to as a follower) are induced by…
An index coding (IC) problem consisting of a server and multiple receivers with different side-information and demand sets can be equivalently represented using a fitting matrix. A scalar linear index code to a given IC problem is a matrix…
Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they…
Circular-shift linear network coding (LNC) is a class of vector LNC with low encoding and decoding complexities, and with local encoding kernels chosen from cyclic permutation matrices. When $L$ is a prime with primitive root $2$, it was…