# Power Efficient IP Lookup with Supernode Caching

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2 Figure 1: Prefixes and corresponding binary trie. Figure 1(a) shows a set of prefixes. The * shown at the right end of each prefix is used neither for the branching described above nor in the length computation. So, the length of P2 is 1. Figure 1(b) shows the binary trie corresponding to this set of prefixes. Shaded nodes correspond to prefixes in the rule table and each contains the next hop for the associated prefix. Tree bitmap (TBM) [] has been proposed to improve the lookup performance of binary tries. In TBM we start with the binary trie for our forwarding table and partition this binary trie into subtries that have at most S levels each. Each partition is then represented as a (TBM) supernode. Figure 2 (a) shows a partitioning of the binary trie of Figure 2 (b) into 4 subtries W-- Z that have 2 levels each. Although a full binary trie with S = 2 levels has 3 nodes, X has only 2 nodes and Y and Z have only one node each. Each partition is represented by a supernode (Figure 2 (b)) that has the following components: 1. A (2 S 1)-bit bit map IBM (internal bitmap) that indicates whether each of the up to 2 S 1 nodes in the partition contains a prefix. The IBM is constructed by superimposing the partition nodes on a full binary trie that has S levels and traversing the nodes of this full binary trie in level order. For node W, the IBM is 1 indicating that the root and its left child have a prefix and the root's right child is either absent or has no prefix. The IBM for X is, which indicates that the left child of the root of X has a prefix and that the right child of the root is either absent or has no prefix (note that the root itself is always present and so a in the leading position of an IBM indicates that the root has no prefix). The IBM's for Y and Z are both. 2. A 2 S -bit EBM (external bit map) that corresponds to the 2 S child pointers that the leaves of a full S-level binary trie has. As was the case for the IBM, we superimpose the nodes of the partition on a full binary trie that has S levels. Then we see which of the partition nodes has child pointers emanating from the leaves of the full binary trie. The EBM for W is 11, which indicates that only the right child of the leftmost leaf of the full binary trie is null. The EBMs for X, Y and Z are indicating that the nodes of X, Y and Z have no children that are not included in X, Y, and Z, respectively. Each child pointer from a node in one partition to a node in another partition becomes a pointer from a supernode to another supercode. To reduce the space required for these intersupernode pointers, the children supernodes of a supernode are Figure 2: TBM for binary trie of Figure 1(b) stored sequentially from left to right so that using the location of the first child and the size of a supernode, we can compute the location of any child supernode. 3. A child pointer that points to the location where the first child supernode is stored. 4. A pointer to a list NH of next-hop data for the prefixes in the partition. NH may have up to 2 S 1 entries. This list is created by traversing the partition nodes in level order. The NH list for W is H1 and H2. The NH list for X is H3. While the NH pointer is part of the supernode, the NH list is not. The NH list is conveniently represented as an array. The NH list (array) of a supernode is stored separate from the supernode itself and is accessed only when the longest matching prefix has been determined and we now wish to determine the next hop associated with this prefix. If we need b bits for a pointer, then a total of 2 S+1 + 2b - 1 bits (plus space for an NH list) are needed for each TBM supernode. Using the IBM, we can determine the longest matching prefix in a supernode; the EBM is used to determine whether we should move next to the first, second, etc. child of the current supernode. If a single memory access is sufficient to retrieve an entire supernode, we can move from one supernode to its child with a single access. The total number of memory accesses to search a supernode trie becomes the number of levels in the supernode trie plus 1 (to access the next hop for the longest matching prefix). III. SUPERNODE CACHING We compress the binary routing table tree into a supernode tree which is stored in low level memory. If a supernode corresponds to an -level subtree, a 32-level binary tree is compressed into a 4-level supernode tree. Assume that each supernode access takes one memory access, the maximum number of memory accesses for an IP lookup is five: it reads three supernodes plus the root nodes and searches the next hop for the longest matching prefix. When the root supernode is always held in cache, this number becomes 4. Obviously, maintaining a small cache will help to reduce the number of memory accesses. Figure 3 illustrates an example of a supernode cache. In this example, the 32-level binary IP routing table is compressed into a 4-level supernode tree. Each supernode contains an - level subtree. The compressed 4-level supernode tree is stored in low level memory. We use a cache to store supernode addresses in low level memory. We store the root (level 1) and X/7/\$2. 7 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE GLOBECOM 7 proceedings.

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