| Summary: | 碩士 === 國立清華大學 === 資訊工程學系 === 90 === We address problem of designing compact routing tables for an n-node unlabeled connected network G. For each node r of G, we are given a spanning tree Tr of G rooted at r. Each node r of G are equipped with ports 1,2,…,dr, where dr is the degree of r in Tr. Each port of r is supposed to be assigned to a neighbor of r in Tr in a one-to-one manner. Suppose that we have the freedom to determine
(a) the node labels of G, and
(b) the assignment of r’s ports to the neighbors of r in Tr.
For each node v of G with v≠r, let pr(v) denote the port of r assigned to s, where s is the neighbor of r in Tr whose removal disconnects v and r in Tr. The requirement of the table design problem is to come up with a compact routing table Rr for each node r of G such that pr(v) can be determined only from Rr and the label of v. Natural objectives of this problem include
1. minimizing the time required to compute the port number of s from Rr;
2. minimizing the bit count of the label of each node;
3. minimizing the bit count of Rr for each node r of G; and
4. minimizing the overall bit count of Rr for all nodes r of G.
Since these objectives are often in conflict, several trade-offs have been shown in the literature. In particular, Gavoille and Hanusse showed in 1999 how to ensure that each Rr spends no more than 8n + o(n) bits, while each pr(v) can be answered from Rr and the label of v in O(log^(2+ε) n) time for any positive constant . In the present paper, we obtain the following improved results:
Result 1: The bit count of each routing table is improved to at most 7.2n+o(n). Each routing decision takes O(log^(2+ε) n) time for any positive constant ε.
Result 2: The overall bit count of all n routing tables is ensured to be no more than 7.05n^2+o(n^2).
Result 3: In the above designs, the label of each node is restricted to be (log n) bits. If the label of each is allowed to be 3(log n) bits, then the bit count of each routing table can be reduced to no more than 7.05n+o(n).
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