An algorithm for linear programming which requires O((m+n)n2 + (m+n)1.5n)L) arithmetic operations
Mathematical Programming: Series A and B
An algebraic approach to network coding
IEEE/ACM Transactions on Networking (TON)
Deterministic network coding by matrix completion
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
The encoding complexity of network coding
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Polynomial time algorithms for multicast network code construction
IEEE Transactions on Information Theory
Improving FPGA routability using network coding
Proceedings of the 18th ACM Great Lakes symposium on VLSI
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Revisiting a secret sharing approach to network codes
ProvSec'12 Proceedings of the 6th international conference on Provable Security
| Hi-index | 754.84 |
In this work, we study the computational perspective of network coding, focusing on two issues. First, we address the computational complexity of finding a network code for acyclic multicast networks. Second, we address the issue of reducing the amount of computation performed by network nodes. In particular, we consider the problem of finding a network code with the minimum possible number of encoding nodes, i.e., nodes that generate new packets by performing algebraic operations on packets received over incoming links. We present a deterministic algorithm that finds a feasible network code for a multicast network over an underlying graph G(V,E) in time O(|E|kh + |V|k2h2 + h4k3(k+h)), where k is the number of destinations and h is the number of packets. Our algorithm improves the best known running time for network code construction. In addition, our algorithm guarantees that the number of encoding nodes in the obtained network code is upper-bounded by O(h3k2). Next, we address the problem of finding integral and fractional network codes with the minimum number of encoding nodes. We prove that in the majority of settings this problem is NP-hard. However, we show that if h = O(1),k = O(1), and the underlying communication graph is acyclic, then there exists an algorithm that solves this problem in polynomial time.