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Improved Compact Routing Tables for Planar Networks via Orderly Spanning Trees

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Computing and Combinatorics (COCOON 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2387))

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Abstract

We address the problem of designing compact routing tables for an unlabeled connected n-node planar network G. For each node r of G, the designer is given a routing spanning tree T r of G rooted at r, which specifies the routes for sending packets from r to the rest of G. Each node r of G is equipped with ports 1,2,...,d r , where d r is the degree of r in T r . Each port of r is supposed to be assigned to a neighbor of r in T r in a one-to-one manner. For each node v of G with υ ≠ r, let portr (υ) be the port to which r should forward packets with destination υ. Under the assumption that the designer has the freedom to determine the label and the port assignment of each node in G, the routing table design problem is to design a compact routing table R r for r such that portr(υ) can be determined only from R r and the label of υ.

Compact routing tables for various network topologies have been extensively studied in the literature. Planar networks are particularly important for routing with geometric metrics. Based upon four-page decompositions of G, Gavoille and Hanusse gave the best previously known result for this problem: Each portr(υ) is computable in O(log2+∈ n) bit operations for any positive constant ɛ; and the number of bits required to encode their R r is at most 8n + o(n). We give a new design that improves the code length of R r to at most 7.181n + o(n) bits without increasing the time required to compute portr(v).

Research supported in part by NSC grant NSC 90-2213-E-001-018. Institute of Information Science, Academia Sinica, 128 Academia Road, Sect. 2, Taipei 115, Taiwan.

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Authors and Affiliations

  1. Academia Sinica, Taiwan

    Hsueh-I Lu

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  1. Hsueh-I Lu
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Editors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, California, 93106, USA

    Oscar H. Ibarra

  2. Department of Mathematics, National University of Singapore, Singapore, Singapore, 117543

    Louxin Zhang

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Lu, HI. (2002). Improved Compact Routing Tables for Planar Networks via Orderly Spanning Trees. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_8

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  • DOI: https://doi.org/10.1007/3-540-45655-4_8

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