Related papers: On the Solvability of 3s/nt Sum-Network---A Region…
In the first paper of this two part communication, we solved in a unified framework a variety of two terminal source coding problems with noncooperative encoders, thereby consolidating works of Shannon, Slepian-Wolf, Wyner,…
This work focuses on the problem of learning an unknown $3$-uniform hypergraph using edge-detecting queries. Our goal is to design a querying strategy that recovers the hyperedge set using as few queries as possible. We restrict our…
A widely used method for solving SOS (Sum Of Squares) decomposition problem is to reduce it to the problem of semi-definite programs (SDPs) which can be efficiently solved in theory. In practice, although many SDP solvers can work out some…
We consider two problems that arise in machine learning applications: the problem of recovering a planted sparse vector in a random linear subspace and the problem of decomposing a random low-rank overcomplete 3-tensor. For both problems,…
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
We study a broad class of algorithmic problems with an "additive flavor" such as computing sumsets, 3SUM, Subset Sum and geometric pattern matching. Our starting point is that these problems can often be solved efficiently for integers,…
We give an algorithm for finding network encoding and decoding equations for error-free multicasting networks with multiple sources and sinks. The algorithm given is efficient (polynomial complexity) and works on any kind of network…
Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing…
Given a graph $G=(V,E)$ and a set of terminal vertices $T$ we say that a superset $S$ of $T$ is $T$-connecting if $S$ induces a connected graph, and $S$ is minimal if no strict subset of $S$ is $T$-connecting. In this paper we prove that…
Since the publication of Shannon's theory of one terminal source coding, a number of interesting extensions have been derived by researchers such as Slepian-Wolf, Wyner, Ahlswede-K\"{o}rner, Wyner-Ziv and Berger-Yeung. Specifically, the…
The $3$SUM hypothesis, the APSP hypothesis and SETH are the three main hypotheses in fine-grained complexity. So far, within the area, the first two hypotheses have mainly been about integer inputs in the Word RAM model of computation. The…
In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time…
This paper considers the problem of distributed source coding for a large network. A major obstacle that poses an existential threat to practical deployment of conventional approaches to distributed coding is the exponential growth of the…
We give a new, constructive uniqueness theorem for tensor decomposition. It applies to order 3 tensors of format $n \times n \times p$ and can prove uniqueness of decomposition for generic tensors up to rank $r=4n/3$ as soon as $p \geq 4$.…
We give new algorithms based on the sum-of-squares method for tensor decomposition. Our results improve the best known running times from quasi-polynomial to polynomial for several problems, including decomposing random overcomplete…
The optimization of joint source and channel coding for a sequence of numerous progressive packets is a challenging problem. Further, the problem becomes more complicated if the space-time coding is also involved with the optimization in a…
We study a new graph separation problem called Multiway Near-Separator. Given an undirected graph $G$, integer $k$, and terminal set $T \subseteq V(G)$, it asks whether there is a vertex set $S \subseteq V(G) \setminus T$ of size at most…
We convert, within polynomial-time and sequential processing, NP-Complete Problems into a problem of deciding feasibility of a given system S of linear equations with constants and coefficients of binary-variables that are 0, 1, or -1. S is…
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…
We propose a simple and fast method for providing a high quality solution for the sum-interference minimization problem. As future networks are deployed in high density urban areas, improved clustering methods are needed to provide low…