Abstract—Most network operators have considered reducing Label Switched Routers (LSR) label spaces (i.e. the number of labels that can be used) as a means of simplifying management of underlaying Virtual Private Networks (VPNs) and, hence, reducing operational expenditure (OPEX). This letter discusses the problem of reducing the label spaces in MultiProtocol Label Switched (MPLS) networks using label merging- better known as MultiPoint-to-Point (MP2P) connections. Because of its origins in IP, MP2P connections have been considered to have treeshapes with Label Switched Paths (LSP) as branches. Due to this fact, previous works by many authors affirm that the problem of minimizing the label space using MP2P in MPLS-theMERGING PROBLEM- cannot be solved optimally with a polynomial algorithm (NP-complete), since it involves a harddecision problem. However, in this letter, the MERGING PROBLEM is analyzed, from the perspective of MPLS, and it is deduced that tree-shapes in MP2P connections are irrelevant. By overriding this tree-shape consideration, it is possible to perform label merging in polynomial time. Based on how MPLS signaling works, this letter proposes an algorithm to compute the minimum number of labels using label merging: the Full Label Merging algorithm. As conclusion, we reclassify the MERGING PROBLEM as Polynomial-solvable, instead of NP-complete. In addition, simulation experiments confirm that without the tree-branch selection problem, more labels can be reduced. Index Terms—Label space reduction, MP2P, label merging,

The recent reduction in telecommunications spending has increased the importance of network planning to improve the return on investment on the existing network infrastructures. Therefore, tools that help in maximizing the bandwidth efficiency of the network at a minimum cost are essential. Previous work in this area focused on increasing bandwidth efficiency and reliability. In this work, in addition to increasing the bandwidth efficiency, we address the complexity of network management and operations. This issue is explicitly addressed by our novel framework, a simple polynomial time algorithm (SimPol)that achieves optimum network performance (in terms of congestion or bandwidth consumption) using only a small number of paths. The problem formulation is based on splittable multicommodity flows. Using SimPol we show that the total number of paths is at most k + m,wherek and m are the numbers of demands and edges in the network, respectively. We extend the basic framework into an integer programming formulation to address the tradeoff between network congestion and the total number of paths. We also use SimPol to address the problem of implementing path/link policies such as bandwidth-limited paths. The performance of SimPol is evaluated through extensive simulations. We find that for large number of demands the LPbased framework provides a near-optimal solution of almost one path per demand. Using the integer programming approach, we can get exactly one path while losing about 10% to 50% in congestion depending on the number of demands. This congestion is, however, far better than the traditional shortest path routing. The framework is general and can be used in capacity planning for transport networks such as MPLS and ATM.

Abstract- Traffic Engineering objective is to optimize network resource utilization. Although several works have been published about minimizing network resource utilization, few works have been focused in LSR label space. This paper proposes an algorithm that gets advantage of the MPLS label stack features in order to reduce the number of labels used in LSPs. Some tunnelling methods and their MPLS implementation drawbacks are also discussed. The described algorithm sets up the NHLFE tables in each LSR creating asymmetric tunnels when possible. Experimental results show that the described algorithm achieves a great reduction factor in the label space. The presented works applies for both types of connections: P2MP and P2P.

Abstract—Most network operators have considered reducing LSR label spaces (number of labels used) as a way of simplifying management of underlaying Virtual Private Networks (VPNs) and therefore reducing operational expenditure (OPEX). The IETF outlined the label merging feature in MPLS—allowing the configuration of MultiPoint-to-Point connections (MP2P)—as a means of reducing label space in LSRs. We found two main drawbacks in this label space reduction scheme: ) it should be separately applied to a set of LSPs with the same egress LSR—which decreases the options for better reductions, and) LSRs close to the edge of the network experience a greater label space reduction than those close to the core. The later implies that MP2P connections reduce the number of labels asymmetrically. In this article we propose a solution to these drawbacks achieved by stacking an additional label onto the packet header. We call this type of reduction Asymmetric Merged Tunnels (AMT). A fast framework for computing the optimal reduction using AMTs is proposed. Our simulations show that the label space can be reduced by up to 20 % more than when label merging is used. Index Terms—Label merging, label space reduction, label stacking, MPLS, multipoint-to-point.

Abstract — Traffic Engineering objective is to optimize network resource utilization. Although several works have been published about minimizing network resource utilization in MPLS networks, few of them have been focused in LSR label space reduction. This letter studies Asymmetric Merged Tunneling (AMT) as a new method for reducing the label space in MPLS network. The proposed method may be regarded as a combination of label merging (proposed in the MPLS architecture) and asymmetric tunneling (proposed recently in our previous works). Finally, simulation results are performed by comparing AMT with both ancestors. They show a great improvement in the label space reduction factor. Index Terms — Label space reduction, MP2P, label merging, asymmetric tunnels, label stack, NHLFE, MPLS traffic engineering. I.

Abstract — Traffic Engineering objective is to optimize network resources utilization. Although several works have been published about minimizing network resource utilization in MPLS networks, few of them have been focused in LSR label space reduction. This work presents a online algorithm that aims to reduce the label space by means of the label stack. Our previous work [ICC2005][ISCC2005] states that using the label stack, so a sort of asymmetric tunnels are built, the label space is reduced considerably. An asymmetric tunnel can be viewed as a Pointto-Point LSP tunnel in which, along its route, more LSPs can be added. In previous work, we discussed such concept and, since there is no a single way to built a tunnel, we presented an offline heuristic (Longest Segment First algorithm) that aims to build tunnels achieving the best label space reduction. In this paper, it is shown that Longest Segment First solutions are weak and, moreover, LSF complexity is high. Hence, we propose an online algorithm named Most Congested Space First (MCSF) that aims to find the best way to make asymmetric tunnels in order to reduce the label space with a set of given LSPs without overriding QoS computed routes. Index Terms — Asymmetric tunnels, label space optimization, label space, label stack, NHLFE, MPLS Traffic Engineering. I.

resource utilization. Although several works have been published about minimizing network resource utilization, few works have been focused in LSR label space. This paper proposes an algorithm that gets advantage of the MPLS label stack features in order to reduce the number of labels used in LSPs. Some tunnelling methods and their MPLS implementation drawbacks are also discussed. The described algorithm sets up the NHLFE tables in each LSR creating asymmetric tunnels when possible. Experimental results show that the described algorithm achieves a great reduction factor in the label space. The presented works applies for both types of connections: P2MP and P2P.

All-Optical Label Switching (AOLS) is a new technology that performs packet forwarding without any optical-electrical-optical conversions. In this paper, we study the problem of routing a set of requests in AOLS networks using GMPLS technology, with the aim of minimizing the number of labels required to ensure the forwarding. We first formalize the problem by associating to each routing strategy a logical hypergraph, called a hypergraph layout, whose hyperarcs are dipaths of the physical graph, called tunnels in GMPLS terminology. We define a cost function for the hypergraph layout, depending on its total length plus its total hop count. Minimizing the cost of the design of an AOLS network can then be expressed as finding a minimum cost hypergraph layout. We prove hardness results for the problem, namely for general directed networks we prove that it is NP-hard to find a C log n-approximation, where C is a positive constant and n is the number of nodes of the network. For symmetric directed networks, we prove that the problem is APX-hard. These hardness results hold even if the traffic instance is a partial broadcast. On the other hand, we provide approximation algorithms, in particular an O(log n)-approximation for symmetric directed networks. Finally, we focus on the case where the physical network is a directed path, providing a polynomial-time dynamic programming algorithm for a fixed number k of sources running in O(n k+2) time.

multiple headers in a single bound:

Abstract- In previous work we proposed a multi-objective traffic engineering scheme (MHDB-S model) using different distribution trees to multicast several flows. In this paper, we propose a heuristic algorithm to create multiple point-to-multipoint (p2mp) LSPs based on the optimum sub-flow values obtained with our MHDB-S model. Moreover, a general problem for supporting multicasting in MPLS networks is the lack of labels. To reduce the number of labels used, a label space reduction algorithm solution is also considered.