A time-optimal distributed arrangement selection algorithm in a line network

This paper defines the distributed arrangement selection problem in a line network in a distributed context and describes the design of a strictly-time-optimal algorithm which solves the problem with a limited local memory space. The problem is regarded as a combined distributed sorting and k-selection problem, namely a problem of sorting elements that are not larger than the kth minimum element in predetermined processes. The algorithm also provides a solution to a resource allocation problem in a line network in a strictly-optimal time.