Xiaofeng Hu

A Fast Algorithm to Find All-Pairs Shortest Paths in Complex Networks

Abstract Finding shortest paths is a fundamental problem in graph theory, which has a large amount of applications in many areas like computer science, operations research, network routing and network analysis. Although many exact and approximate algorithms have been proposed, it is still a time-consuming task to calculate shortest paths for large-scale networks with tremendous volume of data available in recent years. In this paper, we find that the classic Dijkstras algorithm can be improved by simple modification. We propose a fast algorithm which utilize the preiously-calculated results to accelerate the latter calculation. Simple optimization strategies are also proposed with consideration of characteristics of scale-free complex networks. Our experimental results show that the average running time of our algorithm is lower than the Dijkstras algorithm by a factor relating to the connection probability in random networks of ER model. The performance of our algorithm is significantly better than the Dijkstras algorithm in scale-free networks generated by the AB model. The results show that the time complexity is reduced to about O(n 2.4 ) in scalefree complex networks. When the optimization strategies are applied, the algorithm performance is further improved slightly in scale-free networks.

LSC2: An extended link state protocol with centralized control

AbstractCurrent link state routing is based on routing decisions made through distributed interactions among routers. Link state is disseminated by means of flooding, which possesses a few limitations, such as excessive message overhead and network-wide computation. Thus, we propose LSC2, an extended link state routing protocol with centralized control, in this paper to address this problem. In LSC2, link state advertisements (LSAs) are communicated between a centralized element (CE) and a forwarding engine (FE) rather than traditional flooding. Multiple CEs form a separate control network as a representation of the control plane. Through this control network, LSAs are disseminated to FEs in a determinate manner. We also propose a signaling protocol for independent path convergence in the control network, as well as a routing control algorithm to prevent unnecessary routing updates in the forwarding network. We implement a prototype LSC2 and evaluate its performance. Our experiments show that with the use of real topologies, LSC2 can accelerate network convergence and reduce message overhead compared with OSPF. Moreover, LSC2 is robust because having multiple CEs can prevent the occurrence of a single point of failure. LSC2 also scales well with network size by adding additional CEs to share in the processing load.

A Distribute and Geographic Information Based Routing Algorithm for LEO Satellite Constellation Networks

Satellite networks can provide worldwide-coverage wireless data gram services, but cause great challenges for how to efficiently route data gram. The Low Earth Orbit (LEO) satellite is becoming an essential part of the Next-Generation internet with short round-trip delay and low power consumption. In this paper, we propose a routing algorithm for LEO satellite constellation networks with high performance. It needs less memory and computer power, but is capable of highly efficient data gram route. Through simulation we demonstrate the performance of the proposed algorithm. Moreover, we integrate the IP protocol into the algorithm to prove its deploy ability.

Characterization of OSPF Convergence with Correlated Failures

As a popular link state protocol, Open Shortest Path First (OSPF) has been studied for years. A network running OSPF usually takes several tens of seconds to recover from a failure because the protocol timers delay the convergence. In this paper we characterize OSPF convergence behaviors in presence of correlated failures, where the reactive protocol dynamics could be enlarged. Our analysis demonstrates that the interactions between failure detection and routing calculation scheduling could lead to complicated protocol response to correlated failures. We also perform experimental study and the results conform to the analysis. Based on the understanding of OSPF convergence, we present some recommendations for configuring protocol timers in principle.

Towards network convergence and traffic engineering optimization

Faster convergence and optimized traffic engineering are always the pursuits of network operators. However, the link state protocols nowadays have obvious inabilities in achieving these network objectives. In link state network, flooding scheme is usually used to spread the state of link connectivity over the network. Generally, link state flooding introduces various timer configurations for tuning convergence performance. The configuration complexity becomes the major reason of protocol inability to optimize routing convergence. On the other hand, traffic engineering is poorly supported by link state protocol because of temporary status which may cause unexpected traffic migration and packets loss. In this paper, we propose a routing model through which the link state information is disseminated in a globally controllable way. Our model removes existing limitations for accelerating convergence. Meanwhile, our model can integrate traffic engineering into link state protocol by disseminating optimized link weight, thus avoiding the inefficiencies of massive network configurations. Our experiments show that our model can achieve better convergence time and significantly reduce overhead. At the same time, our model is fully scalable with network size. We believe that our model can enhance network convergence and traffic engineering performance simultaneously, as well as prevent unexpected network transitions to improve network reliability.

Constructing Robust Dissemination Paths in Centralized Control Network

With increasing development of forwarding network, the configuration and management of so many distributed devices has become a great challenge. This has motivated a renewed interest in centralized control of routing network. It enables the control-plane functionalities to be centralized on specific network devices in order to separate from packet forwarding. As a result of centralized control, the management information is delivered by dissemination paths between control element and forwarding engines. The construction of dissemination paths is a key component of centralized control, which must be independent of data-plane convergence. Existing approaches are not quite suitable for centralized control network, thus distinct protocols are required. In this paper, we propose an automatic approach to construct robust dissemination paths for centralized control network. We describe the basic procedure of construction with several reasonable optimizations. We also identify how this approach guarantees the robustness of the constructed path, and demonstrate why the approach is operational, flexible and light weighted. The approach can be easily incorporated into any centralized control network systems as an integrated module with minor modifications, thus leveraging their abilities.

A Valley-Free Shortest Path Algorithm and Its Application in Detecting Critical Links among Autonomous Systems

The no-valley and prefer-customer policies are two important routing policies to guarantee the safety and robustness of the inter-domain routing system. Given an AS (Autonomous System) topology, the calculation of shortest paths must consider the two routing policies concurrently. In this paper, we propose a valley-free shortest path algorithm using the classic Dijkstras algorithm framework. The algorithm finds shortest policy paths from other nodes to a specified destination in order to accommodate the routing policies. It is further applied in the problem of detecting critical AS links. A genetic algorithm is designed to find the optimal link set. Using real topology data sets from CAIDA, we evaluate the performance of the proposed algorithms. It turns out that although the routing policies give rise to the complexity in calculating, the time complexity of the algorithm is approximate to the classic algorithm. Additionally, we found that the differences of shortest path lengths with/without the policy constraints are decreasing with the evolution of the Internet. On detecting critical AS links, the genetic algorithm finds critical link sets for AS topologies of four countries. The results have revealed the different robustness of AS topologies for different countries.

Understanding the Influence of Network Topology and Network-layer Naming on the Scalability of Routing

The naming and routing play a very important role for network communications. To characterize the influence of network topology characteristics, network mobility features, network layer naming schemes on the routing scalability, we introduce a new concept called partial transparent graph. We show that a partial transparent graph can better characterize the topological properties of a layered computer network by introducing different kinds of nodes. And we present a routing analysis model to formalize topologies of layered computer networks, network-layer naming, and routing. Then we analyze the routing scalability of two special kinds of naming and routing schemes. We prove that in a static topology with a structured naming, the routing table size can be very small and does not depend on the network size. In a dynamic topology, in which a node can move randomly, the routing table size for name-independent routing with some constraints is linear with the network size.  Index Terms—network architecture, topology, mobility, network naming, name-independent, routing

Characterizing Enough Vantage Points for Pinpointing Routing Instability

Root cause analysis of BGP updates is the key to debug and troubleshoot BGP routing problems. However, inferring the root cause with high accuracy is challenge. Although correlating multiple vantage points is a validate method, how many vantage points are truly necessary to pinpoint the root cause is not resolved. In this paper, we propose a new method to explore two independent vantage points to characterize how many vantage points are enough. Through simulation, we find that our method will largely reduce the number of vantage points which are not necessary to be correlated and the effect of improving the inferring accuracy of our method is the same to correlating all the vantage points.

Locating Routing Instability Based on Path Exploration

Root cause analysis of BGP updates is the key to debug and troubleshoot BGP routing problems. However, accurately inferring what is the cause of routing instability and where it originate is very hard. In this paper, we present a novel approach to locate the origin of routing instability by analyzing the relationship of the closed loops formed by intersecting the all the paths in path exploration and the length variation of the paths received in a single vantage point. Then we demonstrate our approach using BGP data obtained by simulations and show that the method is quite effective. Once there is path exploration when a routing event triggering BGP updates, this approach can precisely identify whether the event is a link failure and pinpoint the right place where the event exactly happens if so. Otherwise the approach can deduce the candidate set of locations to a small size.