Packet filtering plays a critical role in the performance of many network devices such as firewalls, IPSec gateways, DiffServ and QoS routers. A tremendous amount of research was proposed to optimize packet filters. However, most of the related works use deterministic techniques and do not exploit the traffic characteristics in their optimization schemes. In addition, most packet classifiers give no specific consideration for optimizing packet rejection, which is important for many filtering devices like firewalls.

This paper studies the long-standing open question of whether optimal alphabetic binary trees can be constructed in o(n lg n) time. We show that a class of techniques for finding optimal alphabetic trees which includes all current methods yielding O(n lg n) time algorithms are at least as hard as sorting in whatever model of computation is used. We also give O(n) time algorithms for the case where all the input weights are within a constant factor of one another and when they are exponentially separated. 1 Overview The problem of finding optimal alphabetic binary trees can be stated as follows: Given a sequence of n positive weights w 1 ; : : : ; wn , construct a binary tree whose leaves have these weights, such that the tree is optimal with respect to some cost function and also has the property that the weights on the leaves occur in order as the tree is traversed from left to right. A tree which satisfies this last requirement is said to be alphabetic. Although more general cost fu...

Suppose that $S$ is a string of length $m$ drawn from an alphabet of $n$ characters, $d$ of which occur in $S$. Let $P$ be the relative frequency distribution of characters in $S$. We present a new algorithm for dynamic coding that uses at most \(\lceil \lg n \rceil 1\) bits to encode each character in $S$

We describe a modification of the Hu--Tucker algorithm for constructing an optimal alphabetic tree that runs in O(n) time for several classes of inputs. These classes can be described in simple terms and can be detected in linear time. We also give simple conditions and a linear algorithm for determining, in some cases, if two adjacent nodes will be combined in the optimal alphabetic tree.

Binary trees have a wide variety of applications in computer science and information systems. Fast algorithms for building all kinds of binary trees in O(n log n) time do exist. However, no existing algorithm makes it possible to insert in (or delete from) the tree without losing its optimality. In this paper, we propose an algorithm to insert into or delete from a weighted binary alphabetic tree in linear time keeping the tree optimal after insertion or deletion. We show that both insertion and deletion of a node can be done in O(n) time provided its weight is not bigger than the higher weight of its two neighbouring nodes. This algorithm makes it possible to have a dynamic optimal alphabetic tree with reasonable complexity. Key words : Optimal alphabetic trees,insertion and deletion ,linear time alphabetic trees. 1 Introduction Binary trees have received a considerable attention in computer science research. It saves a lot of time to search for data stored in a binary tree structur...

this paper, we presented a simple technique to generate L-restricted alphabetic prefix codes. Furthermore, we proved that the inefficiency of L-restricted alphabetic prefix codes rather than Huffman codes is bounded above by 1+1=/

We shall focus on the following three problems in data structures 1. The Union-find problem. 2. Constructing optimal alphabetic binary trees. 3. The suffix tree. Depending upon the number of students participating we may touch other topics as well.

This functional pearl proposes an ML implementation of the Garsia–Wachs algorithm. This somewhat obscure algorithm builds a binary tree with minimum weighted path length from weighted leaf nodes given in symmetric order. Our solution exhibits the usual benefits of functional programming (use of immutable data structures, pattern-matching, polymorphism) and nicely compares to the purely imperative implementation from The Art of Computer Programming. Categories and Subject Descriptors D.1.1 [Programming Techniques]:

Abstract—Packet matching plays a critical role in the performance of many network devices and a tremendous amount of research has already been invested to come up with better optimized packet filters. However, most of the related works use deterministic techniques and do not exploit the traffic characteristics in their optimization schemes. In addition, most packet classifiers give no specific consideration for optimizing packet rejection, which is important for many filtering devices like firewalls. Our contribution in this paper is twofold. First, we present a novel algorithm for maximizing early rejection of unwanted flows with minimal impact on other flows. Second, we present a new packet filtering dynamic optimization technique that uses statistical search trees to utilize traffic characteristics and minimize the average packet matching time. The proposed techniques timely adapt to changes in the traffic conditions by performing simple calculations for optimizing the search data structure. Our techniques are practically attractive because they exhibit simple-to-implement and easy-to-deploy algorithms. Our extensive evaluation study using Internet traces shows that the proposed techniques can significantly minimize the packet filtering time with reasonable memory space requirements. I.

The aim of this chapter is to present, in appropriate perspective, some selected topics in the theory of variable-length codes. One of the domains of applications is lossless data compression. The main aspects covered include optimal prefix codes and finite automata and transducers. These are a basic tool for encoding and decoding variable-length codes. Connections with codes for constrained channels and sources are developed in some detail. Generating series are used systematically for computing the parameters of encodings such as length and probability distributions. The chapter contains numerous examples and exercises with solutions.