Degree-constrained network flows

Donovan, Peter; Shepherd, Bruce; Vetta, Adrian; Wilfong, Gordon

doi:10.1145/1250790.1250889

Cited by 11 publications

(4 citation statements)

References 9 publications

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“…Confluent flows were investigated in [4], [5], focusing on the problem of determining confluent flows with minimum congestion. A generalization of this problem was investigated in [6], considering d-furcated flows, which are flows with a support graph of maximum outdegree d.…”

Section: Related Workmentioning

confidence: 99%

On the effect of forwarding table size on SDN network utilization

Cohen

Lewin-Eytan

Naor³

et al. 2014

IEEE INFOCOM 2014 - IEEE Conference on Computer Communications

128

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Software Defined Networks (SDNs) are becoming the leading technology behind many traffic engineering solutions, both for backbone and data-center networks, since it allows a central controller to globally plan the path of the flows according to the operator's objective. Nevertheless, networking devices' forwarding table is a limited and expensive resource (e.g., TCAM-based switches) which should thus be considered upon configuring the network. In this paper, we concentrate on satisfying global network objectives, such as maximum flow, in environments where the size of the forwarding table in network devices is limited. We formulate this problem as an (NP-hard) optimization problem and present approximation algorithms for it. We show through extensive simulations that practical use of our algorithms (both in Data Center and backbone scenarios) result in a significant reduction (factor 3) in forwarding table size, while having a small effect on the global objective (maximum flow).

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Section: Related Workmentioning

confidence: 99%

On the effect of forwarding table size on SDN network utilization

Cohen

Lewin-Eytan

Naor³

et al. 2014

IEEE INFOCOM 2014 - IEEE Conference on Computer Communications

128

View full text Add to dashboard Cite

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“…The confluent flow problem was first examined by Chen, Rajaraman and Sundaram [11]. There, and in variants of the problem [10,17,26], the focus was on uncapacitated graphs. 1 The current best result for maximum confluent flow is a factor 3-approximation algorithm for maximum throughput in uncapacitated networks [10].…”

Section: Previous Workmentioning

confidence: 99%

The Inapproximability of Maximum Single-Sink Unsplittable, Priority and Confluent Flow Problems

Shepherd¹,

Vetta²

2015

Preprint

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We consider the single-sink network flow problem. An instance consists of a capacitated graph (directed or undirected), a sink node t and a set of demands that we want to send to the sink. Here demand i is located at a node s i and requests an amount d i of flow capacity in order to route successfully. Two standard objectives are to maximise (i) the number of demands (cardinality) and (ii) the total demand (throughput) that can be routed subject to the capacity constraints. Furthermore, we examine these maximisation problems for three specialised types of network flow: unsplittable, confluent and priority flows.In the unsplittable flow problem, we have edge capacities, and the demand for s i must be routed on a single path. In the confluent flow problem, we have node capacities, and the final flow must induce a tree. Both of these problems have been studied extensively, primarily in the single-sink setting. However, most of this work imposed the no-bottleneck assumption (that the maximum demand d max is at most the minimum capacity u min ). Given the no-bottleneck assumption, there is a factor 4.43-approximation algorithm due to Dinitz et al. [16] for the unsplittable flow problem. Under the even stronger assumption of uniform capacities, there is a factor 3-approximation algorithm due to Chen et al. [10] for the confluent flow problem. However, unlike the unsplittable flow problem, a constant factor approximation algorithm cannot be obtained for the single-sink confluent flow problem even with the no-bottleneck assumption. Specifically, we prove that it is hard in that setting to approximate single-sink confluent flow to within O(log 1− (n)), for any > 0. This result applies for both cardinality and throughput objectives even in undirected graphs.The remainder of our results focus upon the setting without the no-bottleneck assumption. There, the only result we are aware of is an Ω(m 1− ) inapproximability result of Azar and Regev [3] for cardinality single-sink unsplittable flow in directed graphs. We prove this lower bound applies to undirected graphs, including planar networks. This is the first super-constant hardness known for undirected single-sink unsplittable flow, and apparently the first polynomial hardness for undirected unsplittable flow even for general

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“…Theorem 3.2 (The cost of bifurcation; Donovan et al 2007). If a single-sink multicommodity flow has a fractional flow with a maximum node load of U , then there is a bifurcated flow whose maximum node load is U + d max ≤ 2U .…”

Section: Bifurcated and D-furcated Flowsmentioning

confidence: 99%

“…Theorem 3.3 (Cost of bifurcation with unsplit routes from source; Donovan et al 2007). One common approach is to split traffic using source IP address hashing.…”

Section: Bifurcated and D-furcated Flowsmentioning

confidence: 99%