Combinatorics, algorithms, probabilistic and experimental methodologies

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The annotation covers various advanced topics in algorithm design and optimization, including the analysis of the First Fit Decreasing Bin-Packing Algorithm and improvements in linear kernelization for cluster editing. It discusses a deterministic summary structure for update data streams and a refinement algorithm using swarm intelligence for graph bipartitioning. The complexities of the Min-Sum and Min-Max disjoint paths problems are examined, alongside a digital watermarking scheme based on singular value decomposition. The text also introduces a new threshold scheme based on difference equations and explores clique-transversal sets in cubic graphs. It presents approximation algorithms for mixed packing and covering problems, extends the hardness of RNA secondary structure comparison, and addresses the online weighted k-taxi problem. Additionally, it covers topics such as dynamic boundaries in banking default risk modeling, constrained cycle covers in Halin graphs, and optimal semi-online algorithms for scheduling with machine activation costs. Other areas include energy-efficient heuristic scheduling for multimedia services, a fast matching method for DNA sequences, and robust optimization models for uncertain linear programs. The annotation concludes with discussions on market-based service selection in grid computing and heuristic search for 2D NMR alignment, showcasing a wide range of applications in computational theor