### Computational experience with an algorithm for finding the k shortest paths in a network

Douglas R. Shier
1974 Journal of Research of the National Bureau of Standards Section B Mathematical Sciences
A particular co mpute r imple me ntation of th e Doubl e-Sweep method for calcu latin g t.h e k shortes t paths in a net work is described . Res ults are prese nted for a series of co mput ati onal expe rim ent.s perform ed on rectan gular grid network s. Key word s : Double-S weep me thod ; graph ; k s hortes t pa th s; network ; ne twork algorithms; short es t path. The Double-Sweep Method Suppose that G = (.#', d ) is a finite directed network in which the real number iij denotes th e le
more » ... of arc (i, j) Ed joining nodes i , j E.#': Node i of th e arc (i, j) is said to be incident to AMS Subject Cla.ssificalio n: 05035. *Thi s work was done whil e th e aut hor wa s a Na tional Acad e my of Sciences-Natio nal Resea rc h Co un cil Pos td octoral Researc h Associat e at the Nati ona l Burea u of Sta ndards. Was hin gton, D.C. 20234. 1 Fi gures in brac ke ts indicate the lit e rature refe re nces a t th e end of thi s pape r. 2 The algo rithm s prese nt ed in f21 are appropriate for calc ul a tin g k short es t paths be tween all pairs of nod es; beca use of storage limit a tion s, th e appli c at ion of these al goyithm s is limit ed to ne twork s ha ving at most a fe w hundred n o~es. 3 FOR' fRAN V is UNIVAC's au gme nt ed ve rsion of stand ard fORTRAN IV .