Encodings of Multicast Trees

Abstract

Abstract. In this paper, we present efficient ways of encoding multicast trees. Multicast tree encodings provide a convenient way of performing stateless and explicit multicast routing in networks and overlays. We show the correspondence of multicast trees to theoretical tree data structures and give lower bounds on the number of bits needed to represent multicast trees. Our encodings can be used to represent multicast trees using both node identifiers and link indexes and are based on balanced parentheses representation of tree data structures. These encodings are almost space optimal and can be read and processed efficiently. We evaluate the length of these encodings on multicast trees in generated and real topologies.

Distributed Divide-and-Conquer Techniques for Effective DDoS Attack Defenses

“…For a node-labeled tree, the authors propose to also use a pre-order traversal of the node labels, easily represented in m * log(m) bits. Thus, the information-theoretic lower bound for representing a node-labeled binary tree is ≈ m * (2+log(m)) bits [39]. We propose to use the node-labeled balanced parentheses for explicitly ensuring correct association and ordering of immediate children, for every intermediate router.…”

“…Along similar lines of the proposed distributed divide-and-conquer tree construction mechanism, we now encode path frequency distributions as simple tree data structures, and then embed them into the original attack tree, to yield a novel bottom-up attack path frequency tree construction mechanism. Although any frequency encoding and embedding techniques could be used, we evaluate Huffman Encoding [38] and Balanced Parentheses embedding [39] here, as an example.…”

“…In [39], the authors propose an optimal tree representation, needing just 2m bits for compactly representing a m-node tree structure. This optimal representation is obtained by a pre-order tree traversal, producing a "(" while visiting a node for the first time, and a ")" while visiting the node after completely visiting its sub-tree.…”

A composable approach to design of newer techniques for large-scale denial-of-service attack attribution

“…Along similar lines of the proposed distributed divide-and-conquer tree construction mechanism, we now encode path frequency distributions as simple tree data structures, and then embed them into the original attack tree, to yield a novel bottom-up attack path frequency tree construction mechanism. Although any frequency encoding and embedding techniques can be used, we limit our scope here to Huffman encoding [138] and the "balanced parentheses" embedding [139] techniques.…”

“…In [139], the authors propose an optimal tree representation, needing just 2m bits for compactly representing a m-node tree structure. This optimal representation is obtained by a pre-order tree traversal, producing a "(" while visiting a node for the first time, and a ")"…”