Longest Prefix Matching (LPM) is the problem of finding which string from a given set is the longest prefix of another, given string. LPM is a core problem in many applications, including IP routing, network data clustering, and telephone network management. These applications typically require very fast matching of bounded strings, i.e., strings that are short and based on small alphabets. We note a simple correspondence between bounded strings and natural numbers that maps prefixes to nested intervals so that computing the longest prefix matching a string is equivalent to finding the shortest interval containing its corresponding integer value. We then present retries, a fast and compact data structure for LPM on general alphabets. Performance results show that retries outperform previously published data structures for IP look-up. By extending LPM to general alphabets, retries admit new applications that could not exploit prior LPM solutions designed for IP look-ups.

. We study the complexity of a classical combinatorial problem of computing the period of a string. We investigate both the average- and the worst-case complexity of the problem. We deliver almost tight bounds for the average-case. We show that every algorithm computing the period must examine ( p m) symbols of an input string of length m. On the other hand we present an algorithm that computes the period by examining on average O q m log jj m symbols, where jj 2 stands for the input alphabet. We also present a deterministic algorithm that computes the period of a string using m+O(m 3=4 ) comparisons. This is the first algorithm that have the worstcase complexity m+ o(m). 1 Introduction The studies on string periodicity remain a central topic in combinatorial pattern matching due to important applications of periodicity in string searching algorithms, algebra, and in formal language theory (see, e.g., [1, 26, 36, 38, 39]). Let S =< S[1]; S[2]; : : : ; S[m...

Abstract. We study the complexity of a classical combinatorial problem of computing the period of a string. We investigate both the average- and the worst-case complexity of the problem. We deliver almost tight bounds for the average-case. We show that every algorithm computing the period must examine Ω ( √ m) symbols of an input string of length m. On the other hand � we present an�algorithm that computes the period by examining on average O m · log|Σ | m symbols, where |Σ | ≥2 stands for the input alphabet. We also present a deterministic algorithm that computes the period of a string using m + O(m 3/4) comparisons. This is the first algorithm that have the worstcase complexity m + o(m). 1