Performance Guarantees for Approximation Algorithms Depending on Parametrized Triangle Inequalities
SIAM Journal on Discrete Mathematics
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Communication complexity and parallel computing
Communication complexity and parallel computing
Communication complexity
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
P-Complete Approximation Problems
Journal of the ACM (JACM)
Performance guarantees for the TSP with a parameterized triangle inequality
Information Processing Letters
Algorithmics for Hard Problems
Algorithmics for Hard Problems
Stability of Approximation Algorithms for Hard Optimization Problems
SOFSEM '99 Proceedings of the 26th Conference on Current Trends in Theory and Practice of Informatics on Theory and Practice of Informatics
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
The entropic limitations on VLSI computations(Extended Abstract)
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
On taking roots in finite fields
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Reoptimization of the metric deadline TSP
Journal of Discrete Algorithms
Hierarchies of memory limited computations
FOCS '65 Proceedings of the 6th Annual Symposium on Switching Circuit Theory and Logical Design (SWCT 1965)
Algorithmic Aspects of Wireless Sensor Networks
Solving satisfiability in less than 2n steps
Discrete Applied Mathematics
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
On the hardness of reoptimization
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Paired approximation problems and incompatible inapproximabilities
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Improved approximations for TSP with simple precedence constraints
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Parameterized Complexity
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Computer science was born with the formal definition of the notion of an algorithm. This definition provides clear limits of automatization, separating problems into algorithmically solvable problems and algorithmically unsolvable ones. The second big bang of computer science was the development of the concept of computational complexity. People recognized that problems that do not admit efficient algorithms are not solvable in practice. The search for a reasonable, clear and robust definition of the class of practically solvable algorithmic tasks started with the notion of the class ${\mathcal{P}}$ and of ${\mathcal{NP}}$-completeness. In spite of the fact that this robust concept is still fundamental for judging the hardness of computational problems, a variety of approaches was developed for solving instances of ${\mathcal{NP}}$-hard problems in many applications. Our 40-years short attempt to fix the fuzzy border between the practically solvable problems and the practically unsolvable ones partially reminds of the never-ending search for the definition of “life” in biology or for the definitions of matter and energy in physics. Can the search for the formal notion of “practical solvability” also become a never-ending story or is there hope for getting a well-accepted, robust definition of it? Hopefully, it is not surprising that we are not able to answer this question in this invited talk. But to deal with this question is of crucial importance, because only due to enormous effort scientists get a better and better feeling of what the fundamental notions of science like life and energy mean. In the flow of numerous technical results, we must not forget the fact that most of the essential revolutionary contributions to science were done by defining new concepts and notions.