When forming the present participle or verbal noun from the verb to route it is preferable to retain the e in order to distinguish the word from routing, the present participle or verbal noun from rout1, to defeat or rout2, to dig, rummage: the routeing of buses from the city centre to the suburbs. The spelling routing in this sense is, however, sometimes encountered, esp in American English
C13: from Old French rute, from Vulgar Latin rupta via (unattested), literally: a broken (established) way, from Latin ruptus broken, from rumpere to break, burst
early 13c., from O.Fr. rute "road, way, path," from L. rupta (via) "(a road) opened by force," from rupta, fem. pp. of rumpere "to break" (see rupture). Sense of "fixed or regular course for carrying things" (cf. mail route) is 1792, an extension of the meaning "customary path of animals" (early 15c.).