Efficient Algorithms for the Data Exchange Problem

• Published in: IEEE transactions on information theory Vol. 62; no. 4; pp. 1878 - 1896
• Main Authors: Milosavljevic, Nebojsa, Pawar, Sameer, El Rouayheb, Salim, Gastpar, Michael, Ramchandran, Kannan
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Base stations; Codes; combinatorial mathematics; Complexity theory; Efficiency; Electronic mail; Mobile handsets; Network coding; Optimization; packet radio networks; Polynomials; Wireless communication; Network coding; packet radio networks; combinatorial mathematics; optimization
• ISSN: 0018-9448; 1557-9654; 1557-9654
• DOI: 10.1109/TIT.2016.2523980

In this paper, we study the data exchange problem, where a set of users is interested in gaining access to a common file, but where each has only partial knowledge about it as side-information. Assuming that the file is broken into packets, the side-information considered is in the form of linear combinations of the file packets. Given that the collective information of all the users is sufficient to allow recovery of the entire file, the goal is for each user to gain access to the file, while minimizing some communication cost. We assume that the users can communicate over a noiseless broadcast channel, and that the communication cost is a sum of each user's cost function over the number of bits it transmits. For instance, the communication cost could simply be the total number of bits that needs to be transmitted. In the most general case studied in this paper, each user can have any arbitrary convex cost function. We provide deterministic, polynomial-time algorithms (in the number of users and packets), which find an optimal communication scheme that minimizes the communication cost. To further lower the complexity, we also propose a simple randomized algorithm inspired by our deterministic algorithm, which is based on a random linear network-coding scheme.