Abstract-Dynamic routing protocols such as RIP and OSPF essentially implement distributed algorithms for solving the shortest paths problem. The border gateway protocol (BGP) is currently the only interdomain routing protocol deployed in the Internet. BGP does not solve a shortest paths problem since any interdomain protocol is required to allow policy-based metrics to override distance-based metrics and enable autonomous systems to independently define their routing policies with little or no global coordination. It is then natural to ask if BGP can be viewed as a distributed algorithm for solving some fundamental problem. We introduce the stable paths problem and show that BGP can be viewed as a distributed algorithm for solving this problem. Unlike a shortest path tree, such a solution does not represent a global optimum, but rather an equilibrium point in which each node is assigned its local optimum.We study the stable paths problem using a derived structure called a dispute wheel, representing conflicting routing policies at various nodes. We show that if no dispute wheel can be constructed, then there exists a unique solution for the stable paths problem. We define the simple path vector protocol (SPVP), a distributed algorithm for solving the stable paths problem. SPVP is intended to capture the dynamic behavior of BGP at an abstract level. If SPVP converges, then the resulting state corresponds to a stable paths solution. If there is no solution, then SPVP always diverges. In fact, SPVP can even diverge when a solution exists. We show that SPVP will converge to the unique solution of an instance of the stable paths problem if no dispute wheel exists.

The programming language Scheme contains the control construct call/cc that allows access to the current continuation (the current control context). This, in effect, provides Scheme with first-class labels and jumps.We show that the well-known formulae-astypes correspondence, which relates a constructive proof of a formula a to a program of type (Y, can be extended to a typed Idealized Scheme. What is surprising about this correspondence is that it relates classical proofs to typed programs. The existence of computationally interesting "classical programs" -programs of type (Y, where Q holds classically, but not constructively -is illustrated by the definition of conjunctive, disjunctive, and existential types using standard classical definitions. We also prove that all evaluations of typed terms in Idealized Scheme are finite.

The Border Gateway Protocol (BGP) has two distinct modes of operation. External BGP (EBGP) exchanges reachability information between autonomous systems, while Internal BGP (IBGP) exchanges external reachability information within an autonomous system. We study several routing anomalies that are unique to IBGP because, unlike EBGP, forwarding paths and signaling paths are not always symmetric. In particular, we focus on anomalies that can cause the protocol to diverge, and those that can cause a router's chosen forwarding path to an egress point to be deflected by another router on that path. Deflections can greatly complicate the debugging of routing problems, and in the worst case multiple deflections can combine to form persistent forwarding loops. We define a correct IBGP configuration to be one that is anomaly free for every possible set of routes sent by neighboring autonomous systems. We show that determination of IBGP configuration correctness is NP-hard. However, we give simple sufficient conditions on network configurations that guarantee correctness.

The Border Gateway Protocol (BGP)

The Border Gateway Protocol (BGP) is the de facto interdomain routing protocol used to exchange reachability information between Autonomous Systems in the global Internet. BGP is a path-vector protocol that allows each Autonomous System to override distance-based metrics with policy-based metrics when choosing best routes. Varadhan et al. [18] have shown that it is possible for a group of Autonomous Systems to independently define BGP policies that together lead to BGP protocol oscillations that never converge on a stable routing.One approach to addressing this problem is based on static analysis of routing policies to determine if they are safe. We explore the worst-case complexity for convergenceoriented static analysis of BGP routing policies. We present an abstract model of BGP and use it to define several global sanity conditions on routing policies that are related to BGP convergence/divergence.For each condition we show that the complexity of statically checking it is either NP-complete or NP-hard.

No abstract

We study the problem of efficient maintenance of materi-

No abstract