Path-Fault-Tolerant Approximate Shortest-Path Trees

Let $G=(V,E)$ be an $n$-nodes non-negatively real-weighted undirected graph. In this paper we show how to enrich a {\em single-source shortest-path tree} (SPT) of $G$ with a \emph{sparse} set of \emph{auxiliary} edges selected from $E$, in order to create a structure which tolerates effectively a \emph{path failure} in the SPT. This consists of a simultaneous fault of a set $F$ of at most $f$ adjacent edges along a shortest path emanating from the source, and it is recognized as one of the most frequent disruption in an SPT. We show that, for any integer parameter $k \geq 1$, it is possible to provide a very sparse (i.e., of size $O(kn\cdot f^{1+1/k})$) auxiliary structure that carefully approximates (i.e., within a stretch factor of $(2k-1)(2|F|+1)$) the true shortest paths from the source during the lifetime of the failure. Moreover, we show that our construction can be further refined to get a stretch factor of $3$ and a size of $O(n \log n)$ for the special case $f=2$, and that it can be converted into a very efficient \emph{approximate-distance sensitivity oracle}, that allows to quickly (even in optimal time, if $k=1$) reconstruct the shortest paths (w.r.t. our structure) from the source after a path failure, thus permitting to perform promptly the needed rerouting operations. Our structure compares favorably with previous known solutions, as we discuss in the paper, and moreover it is also very effective in practice, as we assess through a large set of experiments.Comment: 21 pages, 3 figures, SIROCCO 201

Survivability issues in WDM optical networks

WDM optical networks make it possible for the bandwidth of transport networks to reach a level on which any failures would cause tremendous data loss and affect a lot of users. Thus, survivability issues of WDM optical networks have attracted a lot of research work. Within the scope of this dissertation, two categories of problems are studied, one is survivable mapping from IP topology to WDM topology, the other is p-cycle protection schemes in WDM networks.;Survivable mapping problem can be described as routing IP links on the WDM topology such that the IP topology stays connected under any single link failure in the WDM topology. This problem has been proved to be NP-complete [1]. At first, this dissertation provides a heuristic algorithm to compute approximated solutions for input IP/WDM topologies as an approach to ease the hardness of it. Then, it examines the problem with a different view, to augment the IP topology so that a survivable mapping can be easily computed. This new perspective leads to an extended survivable mapping problem that is originally proposed and analyzed in this dissertation. In addition, this dissertation also presents some interesting open problems for the survivable mapping problem as future work.;Various protection schemes in WDM networks have been explored. This dissertation focuses on methods based on the p-cycle technology. p-Cycle protection inherits the merit of fast restoration from the link-based protection technology while yielding higher efficiency on spare capacity usage [2]. In this dissertation, we first propose an efficient heuristic algorithm that generates a small subset of candidate cycles that guarantee 100% restorability and help to achieve an efficient design. Then, we adapt p-cycle design to accommodate the protection of the failure of a shared risk link group (SRLG). At last, we discuss the problem of establishing survivable connections for dynamic traffic demands using flow p-cycle

Survivability and performance optimization in communication networks using network coding

The benefits of network coding are investigated in two types of communication networks: optical backbone networks and wireless networks. In backbone networks, network coding is used to improve survivability of the network against failures. In particular, network coding-based protection schemes are presented for unicast and multicast traffic models. In the unicast case, network coding was previously shown to offer near-instantaneous failure recovery at the bandwidth cost of shared backup path protection. Here, cost-effective polynomial-time heuristic algorithms are proposed for online provisioning and protection of unicast traffic. In the multicast case, network coding is used to extend the traditional live backup (1+1) unicast protection to multicast protection; hence called multicast 1+1 protection. It provides instantaneous recovery for single failures in any bi-connected network with the minimum bandwidth cost. Optimal formulation and efficient heuristic algorithms are proposed and experimentally evaluated. In wireless networks, performance benefits of network coding in multicast transmission are studied. Joint scheduling and performance optimization formulations are presented for rate, energy, and delay under routing and network coding assumptions. The scheduling component of the problem is simplified by timesharing over randomly-selected sets of non-interfering wireless links. Selecting only a linear number of such sets is shown to be rate and energy effective. While routing performs very close to network coding in terms of rate, the solution convergence time is around 1000-fold compared to network coding. It is shown that energy benefit of network coding increases as the multicast rate demand is increased. Investigation of energy-rate and delay-rate relationships shows both parameters increase non-linearly as the multicast rate is increased

Route Planning in Transportation Networks

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

Efficient and robust routing of highly variable traffic

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2006.Includes bibliographical references (p. 316-324).Many emerging applications for the Internet are characterized by highly variable traffic behavior over time that is difficult to predict. Classical approaches to network design rely on a model in which a single traffic matrix is estimated. When actual traffic does not conform to such assumptions, desired bandwidth guarantees cannot be provided to the carried traffic. Currently, Internet Service Providers (ISPs) use gross capacity over-provisioning and manual routing adaptation to avoid network congestion caused by unpredictable traffic. These lead to increased network equipment and operational costs. Development of routing infrastructures that optimize network resources while accommodating extreme traffic unpredictability in a robust and efficient manner will be one of the defining themes in the next phase of expansion of the Internet. This thesis proposes two-phase routing as a capacity efficient and robust strategy for handling highly variable traffic. The scheme allows preconfiguration of the network such that all traffic patterns permissible within the network's natural ingress-egress capacity constraints can be routed with bandwidth guarantees without requiring detection of traffic changes in real-time or reconfiguring the network in response to it.(cont.) The scheme routes traffic in two phases -- traffic entering the network is sent from the source to a set of intermediate nodes in predetermined split ratios that depend on the intermediate nodes, and then from the intermediate nodes to the final destination. The scheme has the desirable properties of supporting static optical layer provisioning in IP-over-Optical networks and indirection in specialized service overlay models unlike previous approaches -- like direct source-destination path routing - for handling variable traffic. This thesis represents the first comprehensive study, problem formulation, and algorithm design for many aspects of two-phase routing. Our contributions can be grouped into three broad parts. First, we consider the problems of minimum cost network design and maximum throughput network routing for the scheme. We give a simple solution for minimum cost network design. For maximum throughput network routing. we design linear program.ling based and combinatorial algorithms. We show how the algorithms can handle a total cost constraint for maximum throughput two-phase routing. This can be used to solve the link capacitate version of minimum cost two-phase routing.(cont.) We establish theoretical bounds on the resource requirements of two-phase routing under throughput and cost models with respect to the optimal scheme that is allowed to make the routing dynamically dependent on the current traffic matrix. We also generalize the traffic split ratios to depend not only on the intermediate nodes but also on source and destination of traffic and solve the corresponding optimization problems. Second, we consider making two-phase routing resilient to network failures. Two-phase routing in IP-over-Optical networks can be protected against router node failures through redistribution of traffic split ratio for the failed router node to other intermediate nodes. We propose two different schemes for provisioning the optical layer to handle router node failures. We develop linear programming formulations for both schemes and a fast combinatorial algorithm for the second scheme so as to maximize network throughput. Two-phase routing can be made resilient against link failures by protecting the first and second phase paths using pre-provisioned restoration mechanisms. We consider three such restoration mechanisms - local (link/span) restoration, K-route path restoration, and shared backup path restoration.(cont.) We provide linear programming formulations and combinatorial algorithms for maximum throughput two-phase routing with local restoration and K-route path restoration. We show that the problem of maximum throughput two-phase routing with shared backup path restoration is JVP-hard. Assuming an approximation oracle for a certain disjoint paths problem (which we also show to be AP-hard), we design a combinatorial algorithm with provable guarantees. Third, we consider the application of two-phase routing to multi-hop Wireless Mesh Networks (WMNs). These networks have recently been of much research interest due to their lowered need for wired infrastructure support and due to envisaged new applications like community wireless networks. We extend our optimization framework for maximum throughput two-phase routing in wired networks to handle routing and scheduling constraints that are peculiar to WMNs and arise from the requirement to handle radio transmit/receive diversity and the phenomenon of wireless link interference. We evaluate various aspects of two-phase routing on actual ISP topologies using the developed algorithms. For the WMN application, we use randomly generated WMN topologies for the evaluations.by Sudipta Sengupta.Ph.D

符号化可能なネットワークにおける高信頼経路設計方式

電気通信大学201

Enabling Scalability: Graph Hierarchies and Fault Tolerance

In this dissertation, we explore approaches to two techniques for building scalable algorithms. First, we look at different graph problems. We show how to exploit the input graph\u27s inherent hierarchy for scalable graph algorithms. The second technique takes a step back from concrete algorithmic problems. Here, we consider the case of node failures in large distributed systems and present techniques to quickly recover from these. In the first part of the dissertation, we investigate how hierarchies in graphs can be used to scale algorithms to large inputs. We develop algorithms for three graph problems based on two approaches to build hierarchies. The first approach reduces instance sizes for NP-hard problems by applying so-called reduction rules. These rules can be applied in polynomial time. They either find parts of the input that can be solved in polynomial time, or they identify structures that can be contracted (reduced) into smaller structures without loss of information for the specific problem. After solving the reduced instance using an exponential-time algorithm, these previously contracted structures can be uncontracted to obtain an exact solution for the original input. In addition to a simple preprocessing procedure, reduction rules can also be used in branch-and-reduce algorithms where they are successively applied after each branching step to build a hierarchy of problem kernels of increasing computational hardness. We develop reduction-based algorithms for the classical NP-hard problems Maximum Independent Set and Maximum Cut. The second approach is used for route planning in road networks where we build a hierarchy of road segments based on their importance for long distance shortest paths. By only considering important road segments when we are far away from the source and destination, we can substantially speed up shortest path queries. In the second part of this dissertation, we take a step back from concrete graph problems and look at more general problems in high performance computing (HPC). Here, due to the ever increasing size and complexity of HPC clusters, we expect hardware and software failures to become more common in massively parallel computations. We present two techniques for applications to recover from failures and resume computation. Both techniques are based on in-memory storage of redundant information and a data distribution that enables fast recovery. The first technique can be used for general purpose distributed processing frameworks: We identify data that is redundantly available on multiple machines and only introduce additional work for the remaining data that is only available on one machine. The second technique is a checkpointing library engineered for fast recovery using a data distribution method that achieves balanced communication loads. Both our techniques have in common that they work in settings where computation after a failure is continued with less machines than before. This is in contrast to many previous approaches that---in particular for checkpointing---focus on systems that keep spare resources available to replace failed machines. Overall, we present different techniques that enable scalable algorithms. While some of these techniques are specific to graph problems, we also present tools for fault tolerant algorithms and applications in a distributed setting. To show that those can be helpful in many different domains, we evaluate them for graph problems and other applications like phylogenetic tree inference