ILP formulations for monitoring-cycle design based on segment routing

Abstract

The minimum cycle cover problem in segment routing is to find a set of monitoring cycles such that (a) they originate from the same vantage point, (b) cover every directed link in the network, (c) each cycle can be encoded by a segment list smaller than a given maximum size, and (d) the total length of all cycles is minimized. To solve the problem using Integer Linear Programming (ILP), the key challenge is how to capture all the subtle features of segment routing using linear constraints. In this paper, five original ILP formulations, numbered from ILP1 to ILP5, are designed. In ILP1, the classic flow-based approach is adopted for constructing cycles. In ILP2, a more efficient voltage-based approach is adopted. We then extend ILP2 to ILP3 to jointly minimize the total segment list size. Since the time required to detect a network failure is determined by the longest cycle, we also extend ILP2 to ILP4 to jointly minimize the length of the longest cycle. As finding optimal solutions for large-sized topologies is time-consuming, we propose to limit the set of candidate segments for constructing cycles. Although the resulting ILP5 cannot guarantee optimal solutions, we show that it always outperforms the best heuristic algorithm. Finally, the performance gain of using a dedicated monitoring topology for probe packets, as adopted by all existing heuristic algorithms, is studied.