About the Book

The Stony Brook Algorithm Repository

Steven Skiena
Stony Brook University
Dept. of Computer Science

• By Language
  • C
  • C++
  • C#
  • Java
  • FORTRAN
  • Python
  • Mathematica
  • Pascal
  • ADA
  • Lisp
  • Binary
• By Problem
  • 1.1 Data Structures
    • Dictionaries
    • Priority Queues
    • Suffix Trees and Arrays
    • Graph Data Structures
    • Set Data Structures
    • Kd-Trees
  • 1.2 Numerical Problems
    • Solving Linear Equations
    • Bandwidth Reduction
    • Matrix Multiplication
    • Determinants and Permanents
    • Constrained and Unconstrained Optimization
    • Linear Programming
    • Random Number Generation
    • Factoring and Primality Testing
    • Arbitrary Precision Arithmetic
    • Knapsack Problem
    • Discrete Fourier Transform
  • 1.3 Combinatorial Problems
    • Sorting
    • Searching
    • Median and Selection
    • Generating Permutations
    • Generating Subsets
    • Generating Partitions
    • Generating Graphs
    • Calendrical Calculations
    • Job Scheduling
    • Satisfiability
  • 1.4 Graph Problems -- polynomial-time problems
    • Connected Components
    • Topological Sorting
    • Minimum Spanning Tree
    • Shortest Path
    • Transitive Closure and Reduction
    • Matching
    • Eulerian Cycle / Chinese Postman
    • Edge and Vertex Connectivity
    • Network Flow
    • Drawing Graphs Nicely
    • Drawing Trees
    • Planarity Detection and Embedding
  • 1.5 Graph Problems -- hard problems
    • Clique
    • Independent Set
    • Vertex Cover
    • Traveling Salesman Problem
    • Hamiltonian Cycle
    • Graph Partition
    • Vertex Coloring
    • Edge Coloring
    • Graph Isomorphism
    • Steiner Tree
    • Feedback Edge/Vertex Set
  • 1.6 Computational Geometry
    • Robust Geometric Primitives
    • Convex Hull
    • Triangulation
    • Voronoi Diagrams
    • Nearest Neighbor Search
    • Range Search
    • Point Location
    • Intersection Detection
    • Bin Packing
    • Medial-Axis Transformation
    • Polygon Partitioning
    • Simplifying Polygons
    • Shape Similarity
    • Motion Planning
    • Maintaining Line Arrangements
    • Minkowski Sum
  • 1.7 Set and String Problems
    • Set Cover
    • Set Packing
    • String Matching
    • Approximate String Matching
    • Text Compression
    • Cryptography
    • Finite State Machine Minimization
    • Longest Common Substring
    • Shortest Common Superstring
• Algorithm Links
  • Algorithm Lectures
  • Algorithm Design Manual Information
  • CSE 373 Course page
  • NIST Dictory of Algorithms and Data Structures
  • World of Mathematics
  • Programming Challenges
  • Graduate Study Opportuinties

The matching algorithm used in TRE uses linear worst-case time in the length of the text being searched, and quadratic worst-case time in the length of the used regular expression. In other words, the time complexity of the algorithm is O(M2N), where M is the length of the regular expression and N is the length of the text. The used space is also quadratic on the length of the regex, but does not depend on the searched string. This quadratic behaviour occurs only on pathological cases which are probably very rare in practice.