Kunsoo Park

Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its Applications

We present a linear-time algorithm to compute the longest common prefix information in suffix arrays. As two applications of our algorithm, we show that our algorithm is crucial to the effective use of block-sorting compression, and we present a linear-time algorithm to simulate the bottom-up traversal of a suffix tree with a suffix array combined with the longest common prefix information.

An improved algorithm for approximate string matching

Given a text string, a pattern string, and an integer k, a new algorithm for finding all occurrences of the pattern string in the text string with at most k differences is presented. Both its theoretical and practical variants improve upon the known algorithms.

Linear-time construction of suffix arrays

The time complexity of suffix tree construction has been shown to be equivalent to that of sorting: O(n) for a constant-size alphabet or an integer alphabet and O(n log n) for a general alphabet. However, previous algorithms for constructing suffix arrays have the time complexity of O(n log n) even for a constant-size alphabet. In this paper we present a linear-time algorithm to construct suffix arrays for integer alphabets, which do not use suffix trees as intermediate data structures during its construction. Since the case of a constant-size alphabet can be subsumed in that of an integer alphabet, our result implies that the time complexity of directly constructing suffix arrays matches that of constructing suffix trees.

An accurate worst case timing analysis technique for RISC processors

An accurate and safe estimation of a tasks worst case execution time (WCET) is crucial for reasoning about the timing properties of real-time systems. In RISC processors, the execution time of a program construct (e.g., a statement) is affected by various factors such as cache hits/misses and pipeline hazards, and these factors impose serious problems in analyzing the WCETs of tasks. To analyze the timing effects of RISCs pipelined execution and cache memory, this paper proposes extensions of the original timing schema (Shaw, 1989) where the timing information associated with each program construct is a simple time-bound. We associate with each program construct what we call a WCTA (Worst Case Timing Abstraction), which contains detailed timing information of every execution path that might be the worst case execution path of the program construct. This extension leads to a revised timing schema that is similar to the original timing schema except that concatenation and pruning operations on WCTAs are newly defined to replace the add and max operations on time-bounds in the original timing schema. Our revised timing schema accurately accounts for the timing effects of pipelined execution and cache memory not only within but also across program constructs. This paper also reports on preliminary results of WCET analyses for a pipelined processor. Our results show that up to 50% tighter WCET bounds can be obtained by using the revised timing schema.<<ETX>>

Constructing suffix arrays in linear time

Abstract The time complexity of suffix tree construction has been shown to be equivalent to that of sorting: O ( n ) for a constant-size alphabet or an integer alphabet and O ( n log n ) for a general alphabet. However, previous algorithms for constructing suffix arrays have the time complexity of O ( n log n ) even for a constant-size alphabet. In this paper we present a linear-time algorithm to construct suffix arrays for integer alphabets, which do not use suffix trees as intermediate data structures during its construction. Since the case of a constant-size alphabet can be subsumed in that of an integer alphabet, our result implies that the time complexity of directly constructing suffix arrays matches that of constructing suffix trees.

Dynamic programming with convexity, concavity and sparsity

Abstract Dynamic programming is a general problem-solving technique that has been widely used in various fields such as control theory, operations research, biology and computer science. In many applications dynamic programming problems satisfy additional conditions of convexity, concavity and sparsity. This paper presents a classification of dynamic programming problems and surveys efficient algorithms based on the three conditions.

Truly alphabet-independent two-dimensional pattern matching

A. Amir, G. Benson and M. Farach (see Proc. 24th STOC, p.59-68 (1992)) gave an algorithm for two-dimensional pattern matching (ABF for short) whose text processing is independent of the alphabet and takes O(n/sup 2/) time, but whose pattern processing is dependent on the alphabet and takes O(m/sup 2/log mod Sigma mod ) time. The authors present an algorithm that is truly independent of the alphabet and takes linear O(m/sup 2/+n/sup 2/) time. As in the Knuth-Morris-Pratt algorithm, the only operation on the alphabet is the equality test of two symbols. All previous algorithms except the ABF algorithm reduce the two-dimensional problem into one-dimensional string matching, and use known techniques in string matching. The ABF algorithm uses two-dimensional periodicity for text processing, but their pattern processing resorts to one-dimensional techniques. The authors present a two-dimensional technique for both pattern processing and text processing.<<ETX>>

The consensus string problem for a metric is NP-complete

Given a set S of strings, a consensus string of S based on consensus error is a string w that minimizes the sum of the distances between w and all the strings in S. In this paper, we show that the problem of finding a consensus string based on consensus error is NP-complete when the penalty matrix is a metric.

Parallel Algorithms for Dynamic Programming Recurrences with More Than O(1) Dependency

We study the parallel computation of dynamic programming. We consider four important dynamic programming problems which have wide application, and that have been studied extensively in sequential computation: (1) the 1D problem, (2) the gap problem, (3) the parenthesis problem, and (4) the RNA problem. The parenthesis problem has fast parallel algorithms; almost no work has been done for parallelizing the other three. We present a unifying framework for the parallel computation of dynamic programming recurrences with more than O(1) dependency. We use two well-known methods, the closure method and the matrix product method, as general paradigms for developing parallel algorithms. Combined with various techniques, they lead to a number of new results. Our main results are optimal sublinear-time algorithms for the 1D, parenthesis, and RNA problems.

The influence of the signal dynamics of activated form of IKK on NF-κB and anti-apoptotic gene expressions: A systems biology approach

NF‐κB activation plays a crucial role in anti‐apoptotic responses in response to the apoptotic signaling during tumor necrosis factor (TNF)‐α stimulation. TNF‐α induces apoptosis sensitive to the hepatitis B virus (HBV) infected cells, despite sustained NF‐κB activation. Our results indicate that the HBV infection induces sustained NF‐κB activation, in a manner similar to the TNF‐α stimulation. However, these effects are not merely combined. Computational simulations show that the level of form of the IKK complex activated by phosphorylation (IKK‐p) affects the dynamic pattern of NF‐κB activation during TNF‐α stimulation in the following ways: (i) the initial level of IKK‐p determines the incremental change in IKK‐p at the same level of TNF‐α stimulation, (ii) the incremental change in IKK‐p determines the amplitudes of active NF‐κB oscillation, and (iii) the steady state level of IKK‐p after the incremental change determines the period of active NF‐κB oscillation. Based on experiments, we observed that the initial level of IKK‐p was upregulated and the active NF‐κB oscillation showed smaller amplitudes for a shorter period in HepG2.2.15 cells (HBV‐producing cells) during TNF‐α stimulation, as was indicated by the computational simulations. Furthermore, we found that during TNF‐α stimulation, NF‐κB‐regulated anti‐apoptotic genes were upregulated in HepG2 cells but were downregulated in HepG2.2.15 cells. Based on the previously mentioned results, we can conclude that the IKK‐p‐level changes induced by HBV infection modulate the dynamic pattern of active NF‐κB and thereby could affect NF‐κB‐regulated anti‐apoptotic gene expressions. Finally, we postulate that the sensitive apoptotic response of HBV‐infected cells to TNF‐α stimulation is governed by the dynamic patterns of active NF‐κB based on IKK‐p level changes.