Routing and Capacity Optimization for IP Networks

Bley, Andreas

doi:10.1007/978-3-540-77903-2_2

Cited by 18 publications

(19 citation statements)

References 14 publications

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“…As the conflict inequalities are only necessary to ensure feasibility of the final solution but have no substantial effect on the value of the linear programming relaxation of the master problem, it is not clear, whether it is worth to spend more computation time on a better separation for these inequalities. The computational results reported in [32] and [5] indicate that this is not the case.…”

Section: Client Problemmentioning

confidence: 47%

“…The subpath consistency is one of the simplest conditions that must be satisfied by the paths of an unsplittable shortest path routing. All USPF conflicts that may occur between two paths are in fact violations of the subpath consistency; see [5].…”

Section: Routing Inequalitiesmentioning

confidence: 99%

“…Numerous types of valid inequalities can be derived from the so-called Bellman or subpath consistency condition [2,5]. Two paths P 1 and P 2 are said to satisfy the subpath consistency condition if there are no nodes u and v, such that P 1 and P 2 both contain a subpath P 1 [u, v] and P 2 [u, v], respectively, and P 1 = P 2 .…”

Section: Routing Inequalitiesmentioning

confidence: 99%

“…The independence system I of all unique shortest path forwardings can be extremely complex; see [5]. In general digraphs, the rank quotient of I may be arbitrarily small and the size of irreducible conflicts may be arbitrarily large.…”

Section: Lemma 3 ([5])mentioning

confidence: 99%

“…The main advantage of this decomposition approach is that it permits the use of advanced integer linear programming techniques for unsplittable multi-commodity flow problems to compute provenly optimal routings also for real-world scale problems. An implementation of this algorithm is used successfully in the planning of the German national education and research network for several years [5,10,11]. Modifications of this decomposition approach for shortest multi-path and multicast routing problems are discussed in [12,21,[31][32][33].…”

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confidence: 99%

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An Integer Programming Algorithm for Routing Optimization in IP Networks

Bley¹

2010

Algorithmica

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Most data networks nowadays use shortest path protocols to route the traffic. Given administrative routing lengths for the links of the network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination.In this paper, we present an integer programming algorithm for the minimum congestion unsplittable shortest path routing problem, which arises in the operational planning of such networks. Given a capacitated directed graph and a set of communication demands, the goal is to find routing lengths that define a unique shortest path for each demand and minimize the maximum congestion over all links in the resulting routing. We illustrate the general decomposition approach our algorithm is based on, present the integer and linear programming models used to solve the master and the client problem, and discuss the most important implementational aspects. Finally, we report computational results for various benchmark problems, which demonstrate the efficiency of our algorithm.

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Section: Client Problemmentioning

confidence: 47%

Section: Routing Inequalitiesmentioning

confidence: 99%

Section: Routing Inequalitiesmentioning

confidence: 99%

Section: Lemma 3 ([5])mentioning

confidence: 99%

mentioning

confidence: 99%

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An Integer Programming Algorithm for Routing Optimization in IP Networks

Bley¹

2010

Algorithmica

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Approximability of unsplittable shortest path routing problems

Bley

2009

Networks

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In this article, we discuss the relation of unsplittable shortest path routing (USPR) to other routing schemes and study the approximability of three USPR network planning problems. Given a digraph D = (V , A) and a set K of directed commodities, an USPR is a set of flow paths P * (s,t) , (s, t) ∈ K , such that there exists a metric λ = (λ a ) ∈ Z Z Z A + with respect to which each P * (s,t) is the unique shortest (s, t)-path. In the MinCon-USPR problem, we seek an USPR that minimizes the maximum congestion over all arcs. We show that this problem is N P-hard to approximate within a factor of O(|V | 1− ), but polynomially approximable within min(|A|, |K |) in general and within O(1) if the underlying graph is an undirected cycle or a bidirected ring. We also construct examples where the minimum congestion that can be obtained by USPR is a factor of (|V | 2 ) larger than that achievable by unsplittable flow routing or by shortest multipath routing, and a factor of (|V |) larger than that achievable by unsplittable source-invariant routing. In the CAP-USPR problem, we seek a minimum cost installation of integer arc capacities that admit an USPR of the given commodities. We prove that this problem is N P-hard to approximate within 2 − even in the undirected case, and we devise approximation algorithms for various special cases. The fixed charge network design problem FC-USPR, where the task is to find a minimum cost subgraph of D whose fixed arc capacities admit an USPR of the commodities, is shown to be N POcomplete. All three problems are of great practical interest in the planning of telecommunication networks that are based on shortest path routing protocols. Our results indicate that they are harder than the corresponding unsplittable flow or shortest multi-path routing problems.

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Oblivious OSPF routing with weight optimization under polyhedral demand uncertainty

Altın¹,

Fortz²,

Umit³

2012

Networks

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The desire for configuring well‐managed open shortest path first (OSPF) routes to handle the communication needs in the contemporary business world with larger networks and changing service requirements has opened the way to use traffic engineering tools with the OSPF protocol. Moreover, anticipating possible shifts in expected traffic demands while using network resources efficiently has started to gain more attention. We take these two crucial issues into consideration and study the weight setting problem for OSPF routing problem with polyhedral demands. Our motivation is to optimize the link weight metric such that the minimum cost routing uses shortest paths with equal cost multipath splitting and the routing decisions are robust to possible fluctuations in demands. In addition to a compact mixed integer programming model, we provide an algorithmic approach with two variations to tackle the problem. We present several test results for these two strategies and discuss whether we could make our weight‐managed OSPF comparable to unconstrained routing under polyhedral demand uncertainty. © 2012 Wiley Periodicals, Inc. NETWORKS, 2012

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Routing and Capacity Optimization for IP Networks

Cited by 18 publications

References 14 publications

An Integer Programming Algorithm for Routing Optimization in IP Networks

An Integer Programming Algorithm for Routing Optimization in IP Networks

Approximability of unsplittable shortest path routing problems

Oblivious OSPF routing with weight optimization under polyhedral demand uncertainty

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