On Compact Routing for the Internet

arXiv:0708.2309v1 [cs.NI] 17 Aug 2007 On Compact Routing for the Internet Dmitri Krioukov CAIDA dima@caida.org kc claffy CAIDA kc@caida.org Kevin Fall Intel Research Berkeley kfall@intel.com Arthur Brady Tufts University abrady@cs.tufts.edu ABSTRACT The Internet’s routing system is facing stresses due to its poor fundamental scaling properties. Compact routing is a research field that studies fundamental limits of routing scalability and designs algorithms that try to meet these limits. In particular, compact routing research shows that shortest-path routing, forming a core of traditional routing algorithms, cannot guarantee routing table (RT) sizes that on all network topologies grow slower than linearly as func- tions of the network size. However, there are plenty of com- pact routing schemes that relax the shortest-path require- ment and allow for improved, sublinear RT size scaling that is mathematically provable for all static network topologies. In particular, there exist compact routing schemes designed for grids, trees, and Internet-like topologies that offer RT sizes that scale logarithmically with the network size. In this paper, we demonstrate that in view of recent re- sults in compact routing research, such logarithmic scaling on Internet-like topologies is fundamentally impossible in the presence of topology dynamics or topology-independent (flat) addressing. We use analytic arguments to show that the number of routing control messages per topology change cannot scale better than linearly on Internet-like topologies. We also employ simulations to confirm that logarithmic RT size scaling gets broken by topology-independent address- ing, a cornerstone of popular locator-identifier split propos- als aiming at improving routing scaling in the presence of network topology dynamics or host mobility. These pes- simistic findings lead us to the conclusion that a fundamen- tal re-examination of assumptions behind routing models and abstractions is needed in order to find a routing archi- tecture that would be able to scale “indefinitely.” Categories and Subject Descriptors C.2.2 [Network Protocols]: Routing protocols; G.2.2 [Graph Theory]: Graph algorithms, Network prob- lems; C.2.1 [Network Architecture and Design]: Network topology General Terms Algorithms, Design, Theory Keywords Compact routing, Internet routing, routing scalability 1. INTRODUCTION Despite prevailing concerns among network operators and developers that the current Internet interdomain routing system will not scale to meet the needs of the 21st cen- tury global Internet, networking research has not yet pro- duced a new routing architecture with satisfactory flexibility and mathematically provable scalability characteristics. We believe that we will soon be faced with a critical architec- tural inflection point posing a significant challenge to scaling the size of the future Internet. The last critical point was reached when the Internet’s routing system adopted strong address aggregation using CIDR to handle address scaling in the mid 90’s. While CIDR was an extremely effective tactic, most experts agree that the growth behavior of the routing table in the last decade confirms that the type of address management required by CIDR will not suffice to meet future Internet routing needs, and that a fundamen- tal top-to-bottom reexamination of the routing architecture may be required [1]. In this paper we set to work on such a reexamination.1 As we proceed, we first identify, in Section 2, the fundamen- tal causes of Internet routing scalability problems, and how they imply the need for dramatically more efficient routing algorithms with rigorously proven worst-case performance guarantees. Such algorithms exist—they are known collec- tively as compact routing schemes. They do not and, gener- ally, can not guarantee routing along shortest paths—they stretch them. In Section 3, we juxtapose the formal no- tion of stretch (or hop stretch) with better-known forms of path inflation present in conventional networking. There is a fundamental trade-offbetween stretch and routing ta- ble (RT) size, and we show in Section 4 why hierarchical routing and addressing fall short in finding an optimal bal- ance point of this trade-offfor topologies of interest. We also outline, in the same section, known alternative addressing techniques that compact routing schemes use. We analyze the key ideas behind these schemes in Section 5. We focus on universal schemes in this section and shift our atten- tion to the schemes specialized for Internet-like topologies in Section 6. All these schemes are static. They ignore any communication overhead their implementations might require. We use analytic arguments in Section 7 to directly prove that recent results in compact routing research render 1We clarify up front that scalability is only one of several problems of the current Internet routing architecture. Other problems include security, isolation, configuration control, etc. See [2

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