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Knapsack problems are among the most fundamental problems in optimization. In the Multiple Knapsack problem, we are given multiple knapsacks with different capacities and items with values and sizes. The task is to find a subset of items of…
Multicast remains a fundamental mechanism for scalable content distribution, yet existing approaches face critical limitations. Traditional multicast trees suffer from path redundancy and inefficient utilization of network resources, while…
One major open problem in network coding is to characterize the capacity region of a general multi-source multi-demand network. There are some existing computational tools for bounding the capacity of general networks, but their…
Coded computation is a framework which provides redundancy in distributed computing systems to speed up largescale tasks. Although most existing works assume an error-free scenarios in a master-worker setup, the link failures are common in…
In recent years, network coding has become one of the most interesting fields and has attracted considerable attention from both industry and academia. The idea of network coding is based on the concept of allowing intermediate nodes to…
Coded caching schemes are used to reduce computer network traffics in peak time. To determine the efficiency of the schemes, \cite{MN} defined the information rate of the schemes and gave a construction of optimal coded caching schemes.…
In many problems, the inputs arrive over time, and must be dealt with irrevocably when they arrive. Such problems are online problems. A common method of solving online problems is to first solve the corresponding linear program, and then…
The two-sender unicast index coding problem consists of finding optimal coded transmissions from the two senders which collectively know the messages demanded by all the receivers. Each receiver demands a unique message. One important class…
A moldable job is a job that can be executed on an arbitrary number of processors, and whose processing time depends on the number of processors allotted to it. A moldable job is monotone if its work doesn't decrease for an increasing…
Recently, network error correction coding (NEC) has been studied extensively. Several bounds in classical coding theory have been extended to network error correction coding, especially the Singleton bound. In this paper, following the…
We provide an analytical study of the impact of packet skipping and opportunistic network coding on the timely communication of messages through a single network element. In a first step, we consider a single-server queueing system with…
We consider the multiple unicast problem with three source-terminal pairs over directed acyclic networks with unit-capacity edges. The three $s_i-t_i$ pairs wish to communicate at unit-rate via network coding. The connectivity between the…
Constrained coding is a fundamental field in coding theory that tackles efficient communication through constrained channels. While channels with fixed constraints have a general optimal solution, there is increasing demand for parametric…
In this paper, the problem of designing network codes that are both communicationally and computationally efficient over packet line networks with worst-case schedules is considered. In this context, random linear network codes (dense…
Throughput and per-packet delay can present strong trade-offs that are important in the cases of delay sensitive applications.We investigate such trade-offs using a random linear network coding scheme for one or more receivers in single hop…
We design a cross-layer approach to optimize the joint use of multi-packet reception and network coding, in order to relieve congestion. We construct a model for the behavior of the 802.11 MAC and apply it to several key canonical topology…
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…
In this paper, we study the coding delay and the average coding delay of random linear network codes (dense codes) over line networks with deterministic regular and Poisson transmission schedules. We consider both lossless networks and…
This paper considers the problem of securing a linear network coding system against an adversary that is both an eavesdropper and a jammer. The network is assumed to transport n packets from source to each receiver, and the adversary is…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…