TL;DR
This paper explores decision tree analysis for algorithmic complexity, extending it to clique-finding algorithms in networks, and demonstrates that certain lower bounds are not in P, indicating computational hardness.
Contribution
It introduces a decision tree-based method for analyzing complex algorithms and establishes that some lower bounds are outside P, advancing understanding of computational complexity.
Findings
Decision tree analysis applied to sorting and clique algorithms
Extension of analysis to optimal clique-finding algorithms
Lower bounds for these algorithms are not in P
Abstract
The method for analyzing algorithmic runtime complexity using decision trees is discussed using the sorting algorithm. This method is then extended to optimal algorithms which may find all cliques of size q in network N, or simply the first clique of size q in network N. Finally, the lower bound of such decision trees is demonstrated to not be in P.
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Taxonomy
TopicsFormal Methods in Verification · semigroups and automata theory · Algorithms and Data Compression