A multi-tree routing scheme using acyclic orientations

We propose a mathematical model for fault-tolerant routing based on acyclic orientations, or acorns, of the underlying network G = (V; E). The acorn routing model applies routing tables that store the set of parent pointers associated with each out-neighborhood de ned by the acorn. Unlike the standard single-parent sink-tree model, which is vulnerable to faults, the acorn model a ords a full representation of the entire network and is able to dynamically route around faults. This fault tolerance is achieved when using the acorn model as a multi-tree generator for gathering data at a destination node, as well as an independent tree generator for global point-to-point communication. A fundamental fault-tolerant measure of the model is the capacity of an acorn, i.e., the largest integer k such that each vertex outside the neighborhood N (v) of the destination v has at least k parent pointers. A capacity-k acorn A to destination v is k-vertex fault-tolerant to v. More strongly, we show A supports a k independent sink-tree generator, i.e., the parent pointers of each vertex w ∈ V − N (v) can be partitioned into k nonempty classes labeled 1; 2; : : : ; k such that any set of sink trees T1; T2; : : : ; Tk are pairwise independent, where tree Ti is a sink tree generated by parent pointers labeled i together with the parent pointers into v. We present an linear time optimization algorithm for nding an acorn A of maximum capacity in graphs, based upon a minimax theorem. We also present e cient algorithms that label the parent pointers of capacity-k acorn A, yielding a k-independent sink tree generating scheme. c © 2000 Elsevier Science B.V. All rights reserved. ∗ Corresponding author. E-mail addresses: [email protected] (F.S. Annexstein), [email protected] (K.A. Berman), [email protected] (T.-S. Hsu), [email protected] (R. Swaminathan). 1 Supported in part by an Ohio Board of Regents Research Investment Grant, and NSF Grant No. CCR9877139. 0304-3975/00/$ see front matter c © 2000 Elsevier Science B.V. All rights reserved. PII: S0304 -3975(99)00244 -3 488 F.S. Annexstein et al. / Theoretical Computer Science 240 (2000) 487–494