Related papers: Low-complexity non-uniform demand multicast networ…
Consider a multi-user multi-carrier communication system where multiple users share multiple discrete subcarriers. To achieve high spectrum efficiency, the users in the system must choose their transmit power dynamically in response to fast…
We present a capacity-achieving coding scheme for unicast or multicast over lossy packet networks. In the scheme, intermediate nodes perform additional coding yet do not decode nor even wait for a block of packets before sending out coded…
In the pliable index coding (PICOD) problem, a server is to serve multiple clients, each of which possesses a unique subset of the complete message set as side information and requests a new message which it does not have. The goal of the…
In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…
We establish a duality result between linear index coding and Locally Repairable Codes (LRCs). Specifically, we show that a natural extension of LRCs we call Generalized Locally Repairable Codes (GLCRs) are exactly dual to linear index…
We consider a network multicast example that relates the solvability of the multicast problem with the existence of an entropy function. As a result, we provide an alternative approach to the proving of the insufficiency of linear (and…
We consider the communication capacity of wireline networks for a two-unicast traffic pattern. The network has two sources and two destinations with each source communicating a message to its own destination, subject to the capacity…
Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…
Linearized models of power systems are often desirable to formulate tractable control and optimization problems that still reflect real-world physics adequately under various operating conditions. In this paper, we propose an approach that…
We study a graph coloring problem that is otherwise easy but becomes quite non-trivial in the one-pass streaming model. In contrast to previous graph coloring problems in streaming that try to find an assignment of colors to vertices, our…
The index coding problem is a fundamental transmission problem which occurs in a wide range of multicast networks. Network coding over a large finite field size has been shown to be a theoretically efficient solution to the index coding…
The independent set on a graph $G=(V,E)$ is a subset of $V$ such that no two vertices in the subset have an edge between them. The MIS problem on $G$ seeks to identify an independent set with maximum cardinality, i.e. maximum independent…
Filterless optical transport networks relies on passive optical interconnections between nodes, i.e., on splitters/couplers and amplifiers. While different studies have investigated their design, none of them offer a solution for an optimal…
This work considers the problem of transmitting multiple compressible sources over a network at minimum cost. The aim is to find the optimal rates at which the sources should be compressed and the network flows using which they should be…
In this paper, we use the concept of colored edge graphs to model homogeneous faults in networks. We then use this model to study the minimum connectivity (and design) requirements of networks for being robust against homogeneous faults…
This paper provides a new duality between entropy functions and network codes. Given a function $g\geq 0$ defined on all proper subsets of $N$ random variables, we provide a construction for a network multicast problem which is solvable if…
We show that the following problems are NP-complete. 1. Can the vertex set of a graph be partitioned into two sets such that each set induces a perfect graph? 2. Is the difference between the chromatic number and clique number at most $1$…
We consider the routing flow shop problem with two machines on an asymmetric network. For this problem we discuss properties of an optimal schedule and present a polynomial time algorithm assuming the number of nodes of the network to be…
In the Minimum Clique Routing Problem on Cycles \textsc{MCRPC} we are given a cycle together with a set of demands (weighted origin-destination pairs) and the goal is to route all the pairs minimizing the maximum weighted clique of the…
By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study,…