Parameterized algorithms are a very useful tool for dealing with NP-hard problems on graphs. Yet, to properly utilize parameterized algorithms it is necessary to choose the right parameter based on the type of problem and properties of the target graph class. Tree-width is an example of a very successful graph parameter, however it cannot be used on dense graph classes and there also exist prob...

Much of the difficulty in assessing theories of consciousness stems from their advocates not supplying adequate or convincing characterisations of the phenomenon (or data) they hope to explain. Yet, to make any reasonable assessment this is precisely what is required, for it is not as if our ‘pre-theoretical’ intuitions are philosophically innocent. In what follows, I will attempt to reveal, us...

String problems arise in various applications ranging from text mining to biological sequence analysis. Many string problems are NP-hard. This motivates the search for (fixed-parameter) tractable special cases of these problems. We survey parameterized and multivariate algorithmics results for NP-hard string problems and identify challenges for future research.

We report results from large-scale experiments in satis-ability testing. As has been observed by others, testing the satissability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satissability testing is quite diicult....

Constraint satisfaction problems exhibit a phase transition as a problem parameter is varied, from a region where most problems are easy and soluble to a region where most problems are easy but insoluble. In the intervening phase transition region, the median problem diiculty is greatest. However, in the easy and soluble region, occasional exceptionally hard problems (ehps) can be found, which ...

Randomly-generated constraint satisfaction problems go through a phase transition as the constraint tightness varies. Loose constraints give an `easy-soluble' region, where problems have many solutions and are almost always easy to solve. However, in this region, systematic search algorithms may occasionally encounter problems which are extremely expensive to solve. It has been suggested that i...

One possible escape from the Gibbard-Satterthwaite theorem is computational complexity. For example, it is NP-hard to compute if the STV rule can be manipulated. However, there is increasing concern that such results may not reflect the difficulty of manipulation in practice. In this tutorial, I survey recent results in this area. The Gibbard Satterthwaite theorem proves that, under some simple...

Measure-theoretic aspects of the <:-reducibility structure of the exponential time complexity classes E=DTIME(21inea‘) and E2 = DTIME(2Po’ynomia’) are investigated. Particular attention is given to the complexity (measured b y the size of complexity cores) and distribution (abundance in the sense of measure) of languages that are <:-hard for E and other complexity classes. Tight upper and lower...

We consider parameterised subgraph-counting problems of the following form: given a graph G, how many k-tuples of its vertices have a given property? A number of such problems are known to be #W[1]complete; here we substantially generalise some of these existing results by proving hardness for two large families of such problems. We demonstrate that it is #W[1]-hard to count the number of k-ver...