All of CS161 and the first half of CS261 focus on problems that can be solved in polynomial time. A sad fact is that many practically important and frequently occurring problems do not seem to be polynomial-time solvable, that is, are NP -hard. As an algorithm designer, what does it mean if a problem is NP -hard? After all, a real-world problem doesn’t just go away after you realize that it’s N...

A new approach has been introduced for solving NP-hardness problem in combinatorial optimization problems. Actully, our study focused on the relationship between Lagrange method and Penalty ,this paper introduce a relaxation of fesible region.Furthermore, NP hard tested showed that Augmented Lagrangian Approach outperformed method. Finally, focuses enhancing theoretical convergence features as ...

The complexity, approximation and algorithmic issues of several clustering problems are studied. These non-traditional clustering problems arise from recent studies in microarray data analysis. We prove the following results. (1) Two variants of the Order-Preserving Submatrix problem are NP-hard. There are polynomial-time algorithms for the Order-Preserving Submatrix problem when the condition ...

We formally study two methods for data sanitation that have been used extensively in the database community: k-anonymity and l-diversity. We settle several open problems concerning the difficulty of applying these methods optimally, proving both positive and negative results: – 2-anonymity is in P. – The problem of partitioning the edges of a triangle-free graph into 4-stars (degree-three verti...