We give a (1 + ǫ)-approximate distance oracle with O(1) query time for an undirected planar graph G with n vertices and non-negative edge lengths. For ǫ > 0 and any two vertices u and v in G, our oracle gives a distanced(u, v) with stretch (1 + ǫ) in O(1) time. The oracle has size O(n log n((log n)/ǫ + f (ǫ))) and pre-processing time O(n log n((log 3 n)/ǫ 2 + f (ǫ))), where f (ǫ) = 2 O(1/ǫ) . This is the first (1 + ǫ)-approximate distance oracle with O(1) query time independent of ǫ and the size and pre-processing time nearly linear in n, and improves the query time O(1/ǫ) of previous (1 + ǫ)-approximate distance oracle with size nearly linear in n.

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In this paper, a novel fault-tolerant source routing algorithm for Network on Chip (NOC) called Stochastic Prefix-based Source Routing (SPSR) is proposed. Compared to non-source routing algorithms, it releases the intermediate node from complicated decision-making or routing table maintenance. Unlike the traditional source routing algorithms which use broadcast packets to record the ID of every intermediate node in Route Discovery, it predetermine prospective routes, which can greatly reduces the packets generated and forwarded in the Route Discovery phase, and therefore reduces the power consumption. The proposed routing algorithm is implemented on the open source simulator Nirgam [14], incorporating Orion [15] to estimate the power consumption. Experiment results show that the proposed algorithm can greatly reduce the power consumption in the route discovery and the latency of SPSR is comparable with that of the broadcasting mechanism.