AN O(N LOG2 N) ALGORITHM FOR MAXIMUM FLOW IN UNDIRECTED PLANAR NETWORKS

作     者：HASSIN, R JOHNSON, DB 

作者机构：PENN STATE UNIVDEPT COMP SCIUNIVERSITY PKPA 16802 

出 版 物：《SIAM JOURNAL ON COMPUTING》 (工业与应用数学会计算杂志)

年 卷 期：1985年第14卷第3期

页      面：612-624页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：flow maximum flow planar network duality graph algorithm 

摘      要：A new algorithm is given to find a maximum flow in an undirected planar flow network in $O(n\log ^2 n)$ time, which is faster than the best method previously known by a factor of $\sqrt n /\log n$. The algorithm constructs a transformation of the dual of the given flow network in which differences between shortest distances are equal, under suitable edge correspondences, to edge flows in the given network. The transformation depends on the value of a maximum flow. The algorithm then solves the shortest distances problem efficiently by exploiting certain structural properties of the transformed dual, as well as using a set of cuts constructible in $O(n\log ^2 n)$ time by a known method which is also used to find the requisite flow value. The main result can be further improved by a factor of $\log n/\log^* n$ if a recently developed shortest path algorithm for planar networks is used in place of Dijkstra’s algorithm in each step where shortest paths are computed.