The existence of an envy-free partition has been proved before, but Simmons'proof also yields a constructive approximation algorithm.
42.
Sometimes there are approximation algorithms to the optimization problem, but, using such an approximation might make the mechanism non-truthful.
43.
The results on hardness of approximation described below suggest that there can be no approximation algorithm with an approximation ratio significantly less than linear.
44.
However, under plausible complexity-theoretic assumptions, there is no polynomial-time approximation algorithm with a sub-logarithmic approximation factor.
45.
As with minor-closed graph families of bounded local treewidth, this property has pointed the way to efficient approximation algorithms for these graphs.
46.
The same gadget-based reductions may also be used in the other direction, to transfer approximation algorithms from easier problems to harder problems.
47.
For rectilinear polygons which may contain holes, there is an O ( " log " n " ) factor approximation algorithm.
48.
No approximation algorithms for computing P ( G, x ) are known for any " x " except for the three easy points.
49.
He is married to Dana Ron, who is also a computer scientist at Tel Aviv University, and has collaborated with Ron on approximation algorithms.
50.
The best polynomial-time approximation algorithm known at the moment for this problem achieves a ~ 2.06 approximation by rounding a linear program.
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