Abstract
In the ridesharing problem different people share private vehicles because they have similar itineraries. The objective of solving the ridesharing problem is to minimize the number of drivers needed to carry all load to the destination. The general case of ridesharing problem is NP-complete. For the special case where the network is a chain and the destination is the leftmost vertex of the chain, we present an O(nlogn/logw) time algorithm for the ridesharing problem, where w is the word length used in the algorithm and is at least logn. Previous achieved algorithm for this case requires O(nlogn) time.
Highlights
A road network is expressed by a graph G connecting a set V(G) of vertices and a set E(G) of edges.Each edge (u, v), where u, v are vertices represents a road between u and v
The case considered in this paper is a situation where polynomial time algorithm can be obtained
This version of the ridesharing problem has been studied by Gu, Liang and Zhang
Summary
A road network is expressed by a (undirected) graph G connecting a set V(G) of vertices and a set E(G) of edges. When free(i) > 0 on the path from vi to v0 the driver of trip t can carry additional free(i) load from other trips at vi-1, vi-2, ..., v1. L. & Zhang, G., 2017) are complex and NP-hard because each trip may have many parameters They can be solved as an Integer. The case considered in this paper is a situation where polynomial time algorithm can be obtained. This version of the ridesharing problem has been studied by Gu, Liang and Zhang L. & Zhang, G., 2017) they obtained O(n2) time algorithm for the problem but in
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