TY - GEN

T1 - Network coding

T2 - 2006 40th Annual Conference on Information Sciences and Systems, CISS 2006

AU - Langberg, Michael

AU - Sprintson, Alexander

AU - Bruck, Jehoshua

PY - 2006

Y1 - 2006

N2 - 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 the 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 combining the 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. This improves the best known running time of O(|E|kh + |V|k2h2(k + h)) of Jaggi et al. [1] in the typical case of large communication graphs. In addition, our algorithm guarantees that the number of encoding nodes in the obtained network code is bounded by O(h 3k2). Next, we address the problem of finding a network code with the minimum number of encoding nodes in both integer and fractional coding networks. We prove that in the majority of settings this problem is NP-hard. However, we show that if h = O(1) and k = O(1) and the underlying communication graph is acyclic, then there exists an algorithm that solves this problem in polynomial time.

AB - 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 the 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 combining the 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. This improves the best known running time of O(|E|kh + |V|k2h2(k + h)) of Jaggi et al. [1] in the typical case of large communication graphs. In addition, our algorithm guarantees that the number of encoding nodes in the obtained network code is bounded by O(h 3k2). Next, we address the problem of finding a network code with the minimum number of encoding nodes in both integer and fractional coding networks. We prove that in the majority of settings this problem is NP-hard. However, we show that if h = O(1) and k = O(1) and the underlying communication graph is acyclic, then there exists an algorithm that solves this problem in polynomial time.

UR - http://www.scopus.com/inward/record.url?scp=44049092114&partnerID=8YFLogxK

U2 - 10.1109/CISS.2006.286590

DO - 10.1109/CISS.2006.286590

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AN - SCOPUS:44049092114

SN - 1424403502

SN - 9781424403509

T3 - 2006 IEEE Conference on Information Sciences and Systems, CISS 2006 - Proceedings

SP - 877

EP - 882

BT - 2006 IEEE Conference on Information Sciences and Systems, CISS 2006 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 22 March 2006 through 24 March 2006

ER -