Edge-disjoint routing in plane switch graphs in linear time

By a switch graph we mean an undirected graph G=(P/spl cup//spl dot/W,E) such that all vertices in P (the plugs) have degree one and all vertices in W (the switches) have even degrees. We call G plane if G is planar and can be embedded such that all plugs are in the outer face. Given a set (s/sub 1/,t/sub 1/), ..., (s/sub k/,t/sub k/) of pairs of plugs, the problem is to find edge-disjoint paths p/sub 1/, ..., p/sub k/ such that every p/sub i/ connects s/sub i/ with t/sub i/. The best asymptotic worst case complexity known so far is quadratic in the number of vertices. A linear, and thus asymptotically optimal algorithm is introduced. This result may be viewed as a concluding "key-stone" for a number of previous results on various special cases of the problem.