Efficient Algorithms for the Data Exchange Problem

Abstract

Abstract-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 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.

Cooperative data exchange with weighted cost based on d-basis construction

“…minimum) weighted cost, the corresponding rate vector, and packet index vectors. The complexity of our algorithm is bounded by O(N 3 K 3 log(K)) 1 , which is the same as the complexity of the best-known algorithm for basic CDE problem and significantly lower than the algorithms proposed in [11], [6], [12].…”

“…A randomized algorithm was proposed to estimate the minimum number of required transmissions [5]. Deterministic algorithms based on Dilworth Truncation optimization were proposed to compute the exact minimum number of required transmissions [3], [4], [6]. It has been recently shown that a deterministic algorithm based on conditional basis construction [1] can solve this optimization problem with lower complexity.…”

“…It has been recently shown that a deterministic algorithm based on conditional basis construction [1] can solve this optimization problem with lower complexity. The CDE problem has also been extended in heterogeneous directions, including CDE for arbitrarily connected network [7], [8], successive omniscience and priority [9], [10], and optimization on weighted cost or fairness rate allocations [6], [11], [12].…”

“…In the previously mentioned deterministic algorithms, Dilworth Truncation optimization based algorithms [3], [4], [6] can output the rate vector which can be used to generate linear coding schemes by multicast network code construction algorithm [13] or randomized linear coding generation algorithm [14]. However, conditional basis construction based algorithm [1] can output not only the rate vector but also the packet index vectors, which indicate the packets that should be used to generate linear combinations for transmissions.…”

“…This convexity property of minimum weighted cost function for a fixed sum rate has only been proved for relaxed conditions in [6], where the entries of rate vector can be non-integer.…”