Single failure resiliency in greedy routing

Using greedy routing, network nodes forward packets towards neighbors which are closer to their destination. This approach makes greedy routers significantly more memory-efficient than traditional IP-routers using longest-prefix matching. Greedy embeddings map network nodes to coordinates, such that greedy routing always leads to the destination. Prior works showed that using a spanning tree of the network topology, greedy embeddings can be found in different metric spaces for any graph. However, a single link/node failure might affect the greedy embedding and causes the packets to reach a dead end. In order to cope with network failures, existing greedy methods require large resources and cause significant loss in the quality of the routing (stretch loss). We propose efficient recovery techniques which require very limited resources with minor effect on the stretch. As the proposed techniques are protection, the switch-over takes place very fast. Low overhead, simplicity and scalability of the methods make them suitable for large-scale networks. The proposed schemes are validated on large topologies with properties similar to the Internet. The performances of the schemes are compared with an existing alternative referred as gravity pressure routing

Exploiting the power of multiplicity: a holistic survey of network-layer multipath

The Internet is inherently a multipath network: For an underlying network with only a single path, connecting various nodes would have been debilitatingly fragile. Unfortunately, traditional Internet technologies have been designed around the restrictive assumption of a single working path between a source and a destination. The lack of native multipath support constrains network performance even as the underlying network is richly connected and has redundant multiple paths. Computer networks can exploit the power of multiplicity, through which a diverse collection of paths is resource pooled as a single resource, to unlock the inherent redundancy of the Internet. This opens up a new vista of opportunities, promising increased throughput (through concurrent usage of multiple paths) and increased reliability and fault tolerance (through the use of multiple paths in backup/redundant arrangements). There are many emerging trends in networking that signify that the Internet's future will be multipath, including the use of multipath technology in data center computing; the ready availability of multiple heterogeneous radio interfaces in wireless (such as Wi-Fi and cellular) in wireless devices; ubiquity of mobile devices that are multihomed with heterogeneous access networks; and the development and standardization of multipath transport protocols such as multipath TCP. The aim of this paper is to provide a comprehensive survey of the literature on network-layer multipath solutions. We will present a detailed investigation of two important design issues, namely, the control plane problem of how to compute and select the routes and the data plane problem of how to split the flow on the computed paths. The main contribution of this paper is a systematic articulation of the main design issues in network-layer multipath routing along with a broad-ranging survey of the vast literature on network-layer multipathing. We also highlight open issues and identify directions for future work

Scalable and Efficient Multipath Routing: Complexity and Algorithms

A fundamental unsolved challenge in multipath routing is to provide disjoint end-to-end paths, each one satisfying certain operational goals (e.g., shortest possible), without overwhelming the data plane with prohibitive amount of forwarding state. In this paper, we study the problem of finding a pair of shortest disjoint paths that can be represented by only two forwarding table entries per destination. Building on prior work on minimum length redundant trees, we show that the underlying mathematical problem is NP-complete and we present heuristic algorithms that improve the known complexity bounds from cubic to the order of a single shortest path search. Finally, by extensive simulations we find that it is possible to very closely attain the absolute optimal path length with our algorithms (the gap is just 1–5%), eventually opening the door for wide-scale multipath routing deployments

Hitting and Harvesting Pumpkins

The "c-pumpkin" is the graph with two vertices linked by c>0 parallel edges. A c-pumpkin-model in a graph G is a pair A,B of disjoint subsets of vertices of G, each inducing a connected subgraph of G, such that there are at least c edges in G between A and B. We focus on covering and packing c-pumpkin-models in a given graph: On the one hand, we provide an FPT algorithm running in time 2^O(k) n^O(1) deciding, for any fixed c>0, whether all c-pumpkin-models can be covered by at most k vertices. This generalizes known single-exponential FPT algorithms for Vertex Cover and Feedback Vertex Set, which correspond to the cases c=1,2 respectively. On the other hand, we present a O(log n)-approximation algorithm for both the problems of covering all c-pumpkin-models with a smallest number of vertices, and packing a maximum number of vertex-disjoint c-pumpkin-models.Comment: v2: several minor change

Improving Efficiency and Effectiveness of Multipath Routing in Computer Networks

In this dissertation, we studied methods for improving efficiency and effectiveness of multipath routing in computer networks. We showed that multipath routing can improve network performance for failure recovery, load balancing, Quality of Service (QoS), and energy consumption. We presented a method for reducing the overhead of computing dynamic path metrics, one of the obstacles for implementing dynamic multipath routing in real world networks. In the first part, we proposed a method for building disjoint multipaths that could be used for local failure recovery as well as for multipath routing. Proactive failure recovery schemes have been recently proposed for continuous service of delay-sensitive applications during failure transients at the cost of extra infrastructural support in the form of routing table entries, extra addresses, etc. These extra infrastructure supports could be exploited to build alternative disjoint paths in those frameworks, while keeping the lengths of the alternative paths close to those of the primary paths. The evaluations showed that it was possible to extend the proactive failure recovery schemes to provide support for nearly-disjoint paths which could be employed in multipath routing for load balancing and QoS. In the second part, we proposed a method for reducing overhead of measuring dynamic link state information for multipath routing, specifically path delays used in Wardrop routing. Even when dynamic routing could be shown to offer convergence properties without oscillations, it has not been widely adopted. One of reasons was that the expected cost of keeping the link metrics updated at various nodes in the network. We proposed threshold-based updates to propagate the link state only when the currently measured link state differs from the last updated state consider- ably. Threshold-based updates were shown through analysis and simulations to offer bounded guarantees on path quality while significantly reducing the cost of propagating the dynamic link metric information. The simulation studies indicated that threshold based updates can reduce the number of link updates by up to 90-95% in some cases. In the third part, we proposed methods of using multipath routing for reducing energy consumption in computer networks. Two different approaches have been advocated earlier, from traffic engineering and topology control to hardware-based approaches. We proposed solutions at two different time scales. On a finer time granularity, we employed a method of forwarding through alternate paths to enable longer sleep schedules of links. The proposed schemes achieved more energy saving by increasing the usage of active links and the down time of sleeping links as well as avoiding too frequent link state changes. To the best of our knowledge, this was the first technique combining a routing scheme with hardware scheme to save energy consumption in networks. In our evaluation, alternative forwarding reduced energy consumption by 10% on top of a hardware-based sleeping scheme. On a longer time granularity, we proposed a technique that combined multipath routing with topology control. The proposed scheme achieved increased energy savings by maximizing the link utilization on a reduced topology where the number of active nodes and links are minimized. The proposed technique reduced energy consumption by an additional 17% over previous schemes with single/shortest path routing

Minimum Sum Edge Colorings of Multicycles

In the minimum sum edge coloring problem, we aim to assign natural numbers to edges of a graph, so that adjacent edges receive different numbers, and the sum of the numbers assigned to the edges is minimum. The {\em chromatic edge strength} of a graph is the minimum number of colors required in a minimum sum edge coloring of this graph. We study the case of multicycles, defined as cycles with parallel edges, and give a closed-form expression for the chromatic edge strength of a multicycle, thereby extending a theorem due to Berge. It is shown that the minimum sum can be achieved with a number of colors equal to the chromatic index. We also propose simple algorithms for finding a minimum sum edge coloring of a multicycle. Finally, these results are generalized to a large family of minimum cost coloring problems

Recursive SDN for Carrier Networks

Control planes for global carrier networks should be programmable (so that new functionality can be easily introduced) and scalable (so they can handle the numerical scale and geographic scope of these networks). Neither traditional control planes nor new SDN-based control planes meet both of these goals. In this paper, we propose a framework for recursive routing computations that combines the best of SDN (programmability) and traditional networks (scalability through hierarchy) to achieve these two desired properties. Through simulation on graphs of up to 10,000 nodes, we evaluate our design's ability to support a variety of routing and traffic engineering solutions, while incorporating a fast failure recovery mechanism