TY - GEN

T1 - Compact routing with slack in low doubling dimension

AU - Konjevod, Goran

AU - Richa, Andrea

AU - Xia, Donglin

AU - Yu, Hai

PY - 2007/12/14

Y1 - 2007/12/14

N2 - We consider the problem of compact routing with slack in networks of low doubling dimension. Namely, we seek name-independent routing schemes with (1+) stretch and polylogarithmic storage at each node: since existing lower bound precludes such a scheme, we relax our guarantees to allow for (i) a small fraction of nodes to have large storage, say size of O(n log n) bits, or (ii) a small fraction of source-destination pairs to have larger, but still constant, stretch. In this paper, given any constant (0,1), any (1/ polylog n) and any connected edge-weighted undirected graph G with doubling dimension α O(log log n) and arbitrary node names, we present 1. a (1+)-stretch name-independent routing scheme for G with polylogarithmic packet header size, and with (1-)n nodes storing polylogarithmic size routing tables each and the remaining n nodes storing O(nlog n)-bit routing tables each. 2. a name-independent routing scheme for G with polylogarithmic storage and packet header size, and with stretch (1+) for (1-α n source nodes and (9+) for the remaining α n source nodes.. These results are to be contrasted with our lower bound from PODC 2006, where we showed that stretch 9 is asymptotically optimal for name-independent compact routing schemes in networks of constant doubling dimension.

AB - We consider the problem of compact routing with slack in networks of low doubling dimension. Namely, we seek name-independent routing schemes with (1+) stretch and polylogarithmic storage at each node: since existing lower bound precludes such a scheme, we relax our guarantees to allow for (i) a small fraction of nodes to have large storage, say size of O(n log n) bits, or (ii) a small fraction of source-destination pairs to have larger, but still constant, stretch. In this paper, given any constant (0,1), any (1/ polylog n) and any connected edge-weighted undirected graph G with doubling dimension α O(log log n) and arbitrary node names, we present 1. a (1+)-stretch name-independent routing scheme for G with polylogarithmic packet header size, and with (1-)n nodes storing polylogarithmic size routing tables each and the remaining n nodes storing O(nlog n)-bit routing tables each. 2. a name-independent routing scheme for G with polylogarithmic storage and packet header size, and with stretch (1+) for (1-α n source nodes and (9+) for the remaining α n source nodes.. These results are to be contrasted with our lower bound from PODC 2006, where we showed that stretch 9 is asymptotically optimal for name-independent compact routing schemes in networks of constant doubling dimension.

KW - Compact routing

KW - Doubling dimension

KW - Name-indpendent

UR - http://www.scopus.com/inward/record.url?scp=36849028617&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36849028617&partnerID=8YFLogxK

U2 - 10.1145/1281100.1281113

DO - 10.1145/1281100.1281113

M3 - Conference contribution

AN - SCOPUS:36849028617

SN - 1595936165

SN - 9781595936165

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 71

EP - 80

BT - PODC'07

T2 - PODC'07: 26th Annual ACM Symposium on Principles of Distributed Computing

Y2 - 12 August 2007 through 15 August 2007

ER -