Lower Bounds for Compact
نویسندگان
چکیده
In this paper we present lower bounds for compact routing schemes. We give (1) networks on n vertices which for any interval routing scheme, (n) routers of the network require (n) intervals on some outgoing link and (2) for each d 3, networks of maximal degree d which for any interval routing scheme, (n) routers each require (n= logn) intervals on some outgoing link. Our results give the best known worst-case lower bounds for interval routing. For the case of universal routing schemes we give (3) networks on n vertices which for any near optimal routing scheme with stretch factor < 2 a total of (n 2) memory bits are required, and (4) for each d 3, networks of maximal degree d for which any optimal (resp., near optimal) routing scheme (resp., with stretch factor < 2) requires a total of (n 2 = logn) (resp. (n 2 = log 2 n)) memory bits.
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