O(logW) multidimensional packet classification

We use a collection of hash tables to represent a multidimensional packet classification table. These hash tables are derived from a trie-representation of the multidimensional classifier. The height of this trie is <i>O</i>(<i>W</i>), where <i>W</i> is the sum of the maximum possible length, in bits, of each of the fields of a filter. The leaves at level <i>i</i> of the trie together with markers for some of the leaves at levels <i>j</i> such that <i>j</i> > <i>i</i> are stored in a hash table <i>H<inf>i</inf></i>. The placement of markers is such that a binary search of the <i>H<inf>i</inf></i>'s successfully locates the highest-priority filter that matches any given packet. The number of hash tables equals the trie height, <i>O</i>(<i>W</i>). Hence, a packet may be classified by performing <i>O</i>(log <i>W</i>) hash-table lookups. So the expected lookup-complexity of our data structure for multidimensional packet classification is <i>O</i>(log <i>W</i>). Our proposed scheme affords a memory advantage over the <i>O</i>(log <i>W</i>) 1-D scheme of Waldvogel et al. For multidimensional packet classification, our proposed scheme provides both a time and memory advantage over the extended grid-of-tries scheme of Baboescu et al.

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