Abstract
This paper investigates the MINimum-length-$$k$$k-Disjoint-Paths (MIN-$$k$$k-DP) problem: in a sensor network, given two nodes $$s$$s and $$t$$t, a positive integer $$k$$k, finding $$k$$k (node) disjoint paths connecting $$s$$s and $$t$$t with minimum total length. An efficient distributed algorithm named Optimally-Finding-Disjoint-Paths (OFDP) is proposed for this problem. OFDP guarantees correctness and optimality, i.e., (1) it will find $$k$$k disjoint paths if there exist $$k$$k disjoint paths in the network or the maximum number of disjoint paths otherwise; (2) the disjoint paths it outputs do have minimum total length. To the best of our knowledge, OFDP is the first distributed algorithm that can solve the MIN-$$k$$k-DP problem with correctness and optimality guarantee. Compared with the existing centralized algorithms which also guarantee correctness and optimality, OFDP is shown to be much more efficient by simulation results.
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