Low Cost Sparse Network Monitoring Based on Block Matrix Completion

Due to high network measurement cost, network-wide monitoring faces many challenges. For a network consisting of n nodes, the cost of one time network-wide monitoring will be O(n ² ). To reduce the monitoring cost, inspired by recent progress of matrix completion, a novel sparse network monitoring scheme is proposed to obtain network-wide monitoring data by sampling a few paths while inferring monitoring data of others. However, current sparse network monitoring schemes suffer from the problems of high measurement cost, high computation complexity in sampling scheduling, and long time to recover the un-sampled data. We propose a novel block matrix completion that can guarantee the quality of the un-sampled data inference by selecting as few as m = O(nr ln(r)) samples for a rank r N × T matrix with n = max{N,T}, which largely reduces the sampling complexity as compared to the existing algorithm for matrix completion. Based on block matrix completion, we further propose a light weight sampling scheduling algorithm to select measurement samples and a light weight data inference algorithm to quickly and accurately recover the un-sampled data. Extensive experiments on three real network monitoring data sets verify our theoretical claims and demonstrate the effectiveness of the proposed algorithms.