The complexity of optimization problems
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
A very hard log-space counting class
Theoretical Computer Science - Special issue on structure in complexity theory
The complexity of obtaining solutions for problems in NP and NL
Complexity theory retrospective II
On Syntactic versus Computational Views of Approximability
SIAM Journal on Computing
Structure in Approximation Classes
SIAM Journal on Computing
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Space Efficient Algorithms for Series-Parallel Graphs
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
The Complexity of Finding Paths in Graphs with Bounded Independence Number
SIAM Journal on Computing
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
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This paper introduces logspace optimization problems as analogues of the well-studied polynomial-time optimization problems. Similarly to them, logspace optimization problems can have vastly different approximation properties, even though the underlying decision problems have the same computational complexity. Natural problems, including the shortest path problems for directed graphs, undirected graphs, tournaments, and forests, exhibit such a varying complexity. In order to study the approximability of logspace optimization problems in a systematic way, polynomial-time approximation classes are transferred to logarithmic space. Appropriate reductions are defined and optimization problems are presented that are complete for these classes. It is shown that under the assumption L ≠ NL some logspace optimization problems cannot be approximated with a constant ratio; some can be approximated with a constant ratio, but do not permit a logspace approximation scheme; and some have a logspace approximation scheme, but cannot be solved in logarithmic space. A new natural NL-complete problem is presented that has a logspace approximation scheme.