Space-Efficiency for Routing Schemes of Stretch Factor Three

Improved Compact Routing Schemes for Power-Law Networks

“…For the HDLR + scheme, It's not difficult to see, Equation (1), (2), (3) and (4) also hold according to its forwarding algorithm and routing table setting. This means the HDLR + scheme also has a worst-case stretch (3,0). Besides, we'll prove HDLR + can achieve another stretch (2,D A ).…”

“…Since 1990s, several excellent compact routing schemes are proposed for generic networks [1][2][3] . Both these two schemes are landmarkbased and differ only in how landmarks are selected.…”

“…Cowen scheme adopts a greedy algorithm to find the dominating set of the graph, and obtains the landmark set based on this dominating set, whereas the TZ scheme relies on random techniques for landmark selection. Since Gavoille and Gengler [3] showed that no universal routing scheme with a multiplicative stretch < 3 can produce o(n) routing table size, and Thorup and Zwick [24] proved that any routing scheme with multiplicative stretch strictly below 5 cannot guarantee space smaller than…”

“…Compact routing schemes on arbitrary network topologies (also termed as universal schemes) [1][2][3] and specific networks such as trees [4][5], planar graphs [6], growth bounded graphs [7] and graphs with low doubling dimension [8][9] have attracted wide research attentions. Presently, the most optimized universal compact routing scheme could restrict the routing table size on each node to 1/ 2 ( ) O n 1 bits, and meanwhile, achieve a multiplicative stretch of 3, i.e., the length of the path between any node pair taken by the routing is no more than 3 times the length of the shortest path between the node pair.…”

“…Presently, the most optimized universal compact routing scheme could restrict the routing table size on each node to 1/ 2 ( ) O n 1 bits, and meanwhile, achieve a multiplicative stretch of 3, i.e., the length of the path between any node pair taken by the routing is no more than 3 times the length of the shortest path between the node pair. Although it has been proved that no routing scheme can achieve multiplicative stretch less than 3 with sublinear space for generic networks [3], it is generally believed that routing schemes specialized for peculiar network topologies can achieve better performance than universal ones. This is because, unlike the TZ scheme, specialized routing schemes can exploit the topological properties of special networks.…”