Toward a Model for Backtracking and Dynamic Programming
TOWARD A MODEL FOR BACKTRACKING AND DYNAMIC PROGRAMMING Michael Alekhnovich, Allan Borodin, Joshua Buresh-Oppenheim, Russell Impagliazzo, Avner Magen, and Toniann Pitassi Abstract. We propose a model called priority branching trees (pBT ) for backtrack- ing and dynamic programming algorithms. Our model generalizes both the priority model of Borodin, Nielson and Rackoff, as well as a simple dynamic programming model due to Woeginger, and hence spans a wide spectrum of algorithms. After witnessing the strength of the model, we then show its limitations by providing lower bounds for algorithms in this model for several classical problems such as Interval Scheduling, Knapsack and Satisfiability. Keywords. Greedy Algorithms, Dynamic Programming, Models of Computation, Lower Bounds. Subject classification. 68Q10 1. Introduction The “Design and Analysis of Algorithms” is a basic component of the Computer Science Curriculum. Courses and texts for this topic are often organized around a toolkit of al- gorithmic paradigms or meta-algorithms such as greedy algorithms, divide and conquer, dynamic programming, local search, etc. Surprisingly (as this is often the main “theory course”), these algorithmic paradigms are rarely, if ever, precisely defined. Instead, we provide informal definitional statements followed by (hopefully) well chosen illustrative examples. Our informality in algorithm design should be compared to computability the- ory where we have a well accepted formalization for the concept of an algorithm, namely that provided by Turing machines and its many equivalent computational models (i.e. consider the almost universal acceptance of the Church-Turing thesis). While quantum computation may challenge the concept of “efficient algorithm”, the benefit of having a well defined concept of an algorithm and a computational step is well appreciated.
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