A necessary and sufficient condition for the existence of a complete stable matching
Journal of Algorithms
Fractional kernals in digraphs
Journal of Combinatorial Theory Series B
An analysis of BGP convergence properties
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
The stable paths problem and interdomain routing
IEEE/ACM Transactions on Networking (TON)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Journal of Combinatorial Theory Series B
A fractional model of the border gateway protocol (BGP)
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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The Border Gateway Protocol (BGP) is the interdomain routing protocol used to exchange routing information between Autonomous Systems (ASes) in the internet today. While intradomain routing protocols such as RIP are basically distributed algorithms for solving shortest path problems, the graph theoretic problem that BGP is trying to solve is the stable paths problem (SPP). Unfortunately, unlike shortest path problems, it has been shown that instances of SPP can fail to have a solution, and so BGP can fail to converge. We define a fractional version of SPP and show that all instances of fractional SPP have solutions. We also show that there are polynomial time reductions from a number of well-known graph problems to SPP. For example, finding stable matchings in hypergraphic preference systems (a generalization of graph stable matchings to the case of hypergraphs) and computing kernels in directed graphs are both polynomial time reducible to SPP. These reductions remain valid in the fractional case. Thus the existence of a polynomial time algorithm for computing fractional solutions to SPP would imply polynomial time algorithms for fractional solutions to these other problems as well.