A Linear-Time Algorithm for Edge-Disjoint Paths in Planar Graphs

In th i s paper we discuss the problem of f inding edge-disjoint pa th s in a p lanar , und i rec ted g raph such t h a t each p a t h connec ts two specified vert ices on the b o u n d a r y of the g raph . We will focus on t he "classical" case where an ins tance addi t ional ly fulfills t he so-called evenness-condition. T h e fas tes t a lgor i thm for this p rob lem known from the l i te ra ture requires O (nb/3(loglogn)l/3) t ime, where n denotes the n u m b e r of vertices. In th is paper now, we in t roduce a new approach to th is problem, which resul ts in an O(n) algor i thm. T h e proof of correc tness immed ia t e ly yields an a l te rna t ive proof of the T h e o r e m of O k a m u r a and Seymour , which s t a tes a necessary and sufficient condi t ion for solvability.