MultiProtocol Label Switching (MPLS) [6, 11] is newly proposed routing protocol for the Internet, and is becoming widely popular. In this paper, we initiate a theoretical study of the protocol, and give routing algorithms and lower bounds in a variety of situations. We first study the routing problems on the line. We then build up our results from paths through trees to more general graphs. The basic technique to go to general graphs is that of finding a tree cover, which is a small set of subtrees of the graph such that for each pair of vertices, one of the trees contains an (almost-)shortest path between them. The concept of tree covers appears to have many interesting applications. 1
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