"Design, analysis and theory of algorithms"

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Algorithm design and analysis has seen significant progress in the sophistication of the algorithms being developed as well as in the expanding set of application areas where recent algorithms have become essential. However, algorithm design still remains mainly an art. The goal of this research project is to make algorithm design somewhat more of a science than an art. Namely, we wish to help develop a theory of algorithms that would allow us to better understand the benefits and limitations of general algorithmic approaches as applied to various problem domains. This general project is admittedly both too vague and too ambitious. So in more pragmatic terms, I am studying the power and limitations of well known "conceptually simple meta algorithms" such as greedy algorithms, dynamic programming, primal dual/local ratio algorithms and local search algorithms. To do so, we propose precise models that capture particular instances of such algorithms in relation to a wide variety of problem domains. We proceed to both design and analyze algorithms within a particular framework and as well to establish impossibility results (e.g. inapproximination bounds) with respect to the model. This approach stands in contrast to the fundamental limitations one tries to establish vis a vis complexity bounds (e.g. what can and cannot be computed in polynomial time or logarithmic space). Rather we try to establish limitations independent of complexity issues but instead establish such limitations based on the restricted design of the algorithm. In particular, we prove results that hold whether or not P = NP.