Improving the performance guarantee for approximate graph coloring
Journal of the ACM (JACM)
The complexity of promise problems with applications to public-key cryptography
Information and Control
Computing
NP is as easy as detecting unique solutions
Theoretical Computer Science
Discrete Mathematics - Topics on domination
A taxonomy of complexity classes of functions
Journal of Computer and System Sciences
Journal of Algorithms
An Õ(n3/14)-coloring algorithm for 3-colorable graphs
Information Processing Letters
Unit disk graph recognition is NP-hard
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Algorithmic aspects of constrained unit disk graphs
Algorithmic aspects of constrained unit disk graphs
Online and Offline Distance Constrained Labeling of Disk Graphs
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Improved algorithms for weakly chordal graphs
ACM Transactions on Algorithms (TALG)
Approximation schemes for wireless networks
ACM Transactions on Algorithms (TALG)
Approximating minimum independent dominating sets in wireless networks
Information Processing Letters
Theoretical Computer Science
Location oblivious distributed unit disk graph coloring
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Bidimensionality and geometric graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Integer realizations of disk and segment graphs
Journal of Combinatorial Theory Series B
European Journal of Combinatorics
Approximating 2-cliques in unit disk graphs
Discrete Applied Mathematics
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We introduce a new definition of efficient algorithms for restricted domains. Under this definition, an algorithm is required to be "robust," i.e., it must produce correct output regardless of whether the input actually belongs to the restricted domain or not. This is to be contrasted with the "promise" version of solving problems on restricted domains, in which there is a guarantee that the input is in the class, and an algorithm to "solve" the problem need not function correctly or even terminate if this guarantee is not met. There exist problems that have a polynomial time promise solution, while being NP-hard if required to be robust. We show perhaps the surprising result that robustly finding a maximum independent set in a well-covered graph (i.e., a graph in which every maximal independent set is of the same size) is NP-hard. An argument can be made that this hardness result is more meaningful than the trivial polynomial time promise algorithm. We give a polynomial time robust algorithm for the maximum clique problem in unit disk graphs, i.e., given an input graph G in general form, the output is either a maximum clique for G or a certificate that G is not a unit disk graph. The existence of this algorithm is to be reconciled with the apparent contradiction posed by the facts: (1) Recognizing whether an input graph given in general form is a unit disk graph is NP-hard; in fact, it is not even known to be in NP. (2) Finding a maximum clique in an input graph given in general form is NP-hard.