On the Comparison Complexity of the String Prefix-Matching Problem

In this paper we study the exact comparison complexity of the stringprefix-matching problem in the deterministic sequential comparison modelwith equality tests. We derive almost tight lower and upper bounds onthe number of symbol comparisons required in the worst case by on-lineprefix-matching algorithms for any fixed pattern and variable text. Unlikeprevious results on the comparison complexity of string-matching andprefix-matching algorithms, our bounds are almost tight for any particular pattern.We also consider the special case where the pattern and the text are thesame string. This problem, which we call the string self-prefix problem, issimilar to the pattern preprocessing step of the Knuth-Morris-Pratt string-matchingalgorithm that is used in several comparison efficient string-matchingand prefix-matching algorithms, including in our new algorithm.We obtain roughly tight lower and upper bounds on the number of symbolcomparisons required in the worst case by on-line self-prefix algorithms.Our algorithms can be implemented in linear time and space in thestandard uniform-cost random-access-machine model

Exact string matching algorithms : survey, issues, and future research directions

String matching has been an extensively studied research domain in the past two decades due to its various applications in the fields of text, image, signal, and speech processing. As a result, choosing an appropriate string matching algorithm for current applications and addressing challenges is difficult. Understanding different string matching approaches (such as exact string matching and approximate string matching algorithms), integrating several algorithms, and modifying algorithms to address related issues are also difficult. This paper presents a survey on single-pattern exact string matching algorithms. The main purpose of this survey is to propose new classification, identify new directions and highlight the possible challenges, current trends, and future works in the area of string matching algorithms with a core focus on exact string matching algorithms. © 2013 IEEE

Design and Evaluation of Packet Classification Systems, Doctoral Dissertation, December 2006

Although many algorithms and architectures have been proposed, the design of efficient packet classification systems remains a challenging problem. The diversity of filter specifications, the scale of filter sets, and the throughput requirements of high speed networks all contribute to the difficulty. We need to review the algorithms from a high-level point-of-view in order to advance the study. This level of understanding can lead to significant performance improvements. In this dissertation, we evaluate several existing algorithms and present several new algorithms as well. The previous evaluation results for existing algorithms are not convincing because they have not been done in a consistent way. To resolve this issue, an objective evaluation platform needs to be developed. We implement and evaluate several representative algorithms with uniform criteria. The source code and the evaluation results are both published on a web-site to provide the research community a benchmark for impartial and thorough algorithm evaluations. We propose several new algorithms to deal with the different variations of the packet classification problem. They are: (1) the Shape Shifting Trie algorithm for longest prefix matching, used in IP lookups or as a building block for general packet classification algorithms; (2) the Fast Hash Table lookup algorithm used for exact flow match; (3) the longest prefix matching algorithm using hash tables and tries, used in IP lookups or packet classification algorithms;(4) the 2D coarse-grained tuple-space search algorithm with controlled filter expansion, used for two-dimensional packet classification or as a building block for general packet classification algorithms; (5) the Adaptive Binary Cutting algorithm used for general multi-dimensional packet classification. In addition to the algorithmic solutions, we also consider the TCAM hardware solution. In particular, we address the TCAM filter update problem for general packet classification and provide an efficient algorithm. Building upon the previous work, these algorithms significantly improve the performance of packet classification systems and set a solid foundation for further study

Algorithms and Architectures for Network Search Processors

The continuous growth in the Internet’s size, the amount of data traffic, and the complexity of processing this traffic gives rise to new challenges in building high-performance network devices. One of the most fundamental tasks performed by these devices is searching the network data for predefined keys. Address lookup, packet classification, and deep packet inspection are some of the operations which involve table lookups and searching. These operations are typically part of the packet forwarding mechanism, and can create a performance bottleneck. Therefore, fast and resource efficient algorithms are required. One of the most commonly used techniques for such searching operations is the Ternary Content Addressable Memory (TCAM). While TCAM can offer very fast search speeds, it is costly and consumes a large amount of power. Hence, designing cost-effective, power-efficient, and high-speed search techniques has received a great deal of attention in the research and industrial community. In this thesis, we propose a generic search technique based on Bloom filters. A Bloom filter is a randomized data structure used to represent a set of bit-strings compactly and support set membership queries. We demonstrate techniques to convert the search process into table lookups. The resulting table data structures are kept in the off-chip memory and their Bloom filter representations are kept in the on-chip memory. An item needs to be looked up in the off-chip table only when it is found in the on-chip Bloom filters. By filtering the off-chip memory accesses in this fashion, the search operations can be significantly accelerated. Our approach involves a unique combination of algorithmic and architectural techniques that outperform some of the current techniques in terms of cost-effectiveness, speed, and power-efficiency

On using content addressable memory for packet classification

Packet switched networks such as the Internet require packet classification at every hop in order to ap-ply services and security policies to traffic flows. The relentless increase in link speeds and traffic volume imposes astringent constraints on packet classification solutions. Ternary Content Addressable Memory (TCAM) devices are favored by most network component and equipment vendors due to the fast and de-terministic lookup performance afforded by their use of massive parallelism. While able to keep up with high speed links, TCAMs suffer from exorbitant power consumption, poor scalability to longer search keys and larger filter sets, and inefficient support of multiple matches. The research community has responded with algorithms that seek to meet the lookup rate constraint with greater efficiency through the use of com-modity Random Access Memory (RAM) technology. The most promising algorithms efficiently achieve high lookup rates by leveraging the statistical structure of real filter sets. Due to their dependence on filter set characteristics, it is difficult to provision processing and memory resources for implementations that support a wide variety of filter sets. We show how several algorithmic advances may be leveraged to im-prove the efficiency, scalability, incremental update and multiple match performance of CAM-based packet classification techniques without degrading the lookup performance. Our approach, Label Encoded Content Addressable Memory (LECAM), represents a hybrid technique that utilizes decomposition, label encoding, and a novel Content Addressable Memory (CAM) architecture. By reducing the number of implementation parameters, LECAM provides a vehicle to carry several of the recent algorithmic advances into practice. We provide a thorough overview of CAM technologies and packet classification algorithms, along with a detailed discussion of the scaling issues that arise with longer search keys and larger filter sets. We also provide a comparative analysis of LECAM and standard TCAM using a collection of real and synthetic filter sets of various sizes and compositions

String Indexing for Patterns with Wildcards

We consider the problem of indexing a string $t$ of length $n$ to report the occurrences of a query pattern $p$ containing $m$ characters and $j$ wildcards. Let $occ$ be the number of occurrences of $p$ in $t$, and $\sigma$ the size of the alphabet. We obtain the following results. - A linear space index with query time $O(m+\sigma^j \log \log n + occ)$. This significantly improves the previously best known linear space index by Lam et al. [ISAAC 2007], which requires query time $\Theta(jn)$ in the worst case. - An index with query time $O(m+j+occ)$ using space $O(\sigma^{k^2} n \log^k \log n)$, where $k$ is the maximum number of wildcards allowed in the pattern. This is the first non-trivial bound with this query time. - A time-space trade-off, generalizing the index by Cole et al. [STOC 2004]. We also show that these indexes can be generalized to allow variable length gaps in the pattern. Our results are obtained using a novel combination of well-known and new techniques, which could be of independent interest

Data Structures and Algorithms for Scalable NDN Forwarding

Named Data Networking (NDN) is a recently proposed general-purpose network architecture that aims to address the limitations of the Internet Protocol (IP), while maintaining its strengths. NDN takes an information-centric approach, focusing on named data rather than computer addresses. In NDN, the content is identified by its name, and each NDN packet has a name that specifies the content it is fetching or delivering. Since there are no source and destination addresses in an NDN packet, it is forwarded based on a lookup of its name in the forwarding plane, which consists of the Forwarding Information Base (FIB), Pending Interest Table (PIT), and Content Store (CS). In addition, as an in-network caching element, a scalable Repository (Repo) design is needed to provide large-scale long-term content storage in NDN networks. Scalable NDN forwarding is a challenge. Compared to the well-understood approaches to IP forwarding, NDN forwarding performs lookups on packet names, which have variable and unbounded lengths, increasing the lookup complexity. The lookup tables are larger than in IP, requiring more memory space. Moreover, NDN forwarding has a read-write data plane, requiring per-packet updates at line rates. Designing and evaluating a scalable NDN forwarding node architecture is a major effort within the overall NDN research agenda. The goal of this dissertation is to demonstrate that scalable NDN forwarding is feasible with the proposed data structures and algorithms. First, we propose a FIB lookup design based on the binary search of hash tables that provides a reliable longest name prefix lookup performance baseline for future NDN research. We have demonstrated 10 Gbps forwarding throughput with 256-byte packets and one billion synthetic forwarding rules, each containing up to seven name components. Second, we explore data structures and algorithms to optimize the FIB design based on the specific characteristics of real-world forwarding datasets. Third, we propose a fingerprint-only PIT design that reduces the memory requirements in the core routers. Lastly, we discuss the Content Store design issues and demonstrate that the NDN Repo implementation can leverage many of the existing databases and storage systems to improve performance

Longest Common Substring and Longest Palindromic Substring in O~(n)\tilde{\mathcal{O}}(\sqrt{n}) Time

The Longest Common Substring (LCS) and Longest Palindromic Substring (LPS) are classical problems in computer science, representing fundamental challenges in string processing. Both problems can be solved in linear time using a classical model of computation, by means of very similar algorithms, both relying on the use of suffix trees. Very recently, two sublinear algorithms for LCS and LPS in the quantum query model have been presented by Le Gall and Seddighin~\cite{GallS23}, requiring $\tilde{\mathcal{O}}(n^{5/6})$ and $\tilde{\mathcal{O}}(\sqrt{n})$ queries, respectively. However, while the query model is fascinating from a theoretical standpoint, its practical applicability becomes limited when it comes to crafting algorithms meant for actual execution on real hardware. In this paper we present, for the first time, a $\tilde{\mathcal{O}}(\sqrt{n})$ quantum algorithm for both LCS and LPS working in the circuit model of computation. Our solutions are simpler than previous ones and can be easily translated into quantum procedures. We also present actual implementations of the two algorithms as quantum circuits working in $\mathcal{O}(\sqrt{n}\log^5(n))$ and $\mathcal{O}(\sqrt{n}\log^4(n))$ time, respectively