Combinatorial reconstruction problems

Combinatorial reconstruction problems

Let X be a (finite or infinite) set and let G be a (finite or infinite) group of automorphisms of X. Thus G acts on X and for every g E G the sequence k&x is a permutation of X. For every subset Y of X and every g E G, let g Y be the set of all elements gy, for y E Y. Clearly 1 g Y 1 = 1 Y 1 for every finite Y, and this defines an action of the group G on the power set of X. The orbit of a subs...

Reducibility Among Combinatorial Problems

Combinatorial Reconstruction of Sibling Relationships

We present a new algorithm for reconstructing sibling relationships in a single generation of individuals without parental information, using data from codominant DNA markers such as microsatellites. We use the simple genetic constraints on the full-sibling groups, imposed by the Mendelian inheritance rules, and combinatorial optimization techniques to extract a minimum number of consistent sib...

Combinatorial feature selection problems

Motivated by frequently recurring themes in information retrieval and related disciplines, we define a genre of problems called combinatorial feature selection problems. Given a set S of multidimensional objects, the goal is to select a subset K of relevant dimensions (or features) such that some desired property holds for the set S restricted to K. Depending on , the goal could be to either ma...

On combinatorial testing problems

We study a class of hypothesis testing problems in which, upon observing the realization of an ndimensional Gaussian vector, one has to decide whether the vector was drawn from a standard normal distribution or, alternatively, whether there is a subset of the components belonging to a certain given class of sets whose elements have been “contaminated,” that is, have a mean different from zero. ...