Cuts and bounds

Cuts and bounds

Weconsider the colouring (or homomorphism) orderC induced by all finite graphs and the existence of a homomorphism between them. This ordering may be seen as a lattice which is far from being complete. In this paper we study bounds and suprema and maximal elements in C of some frequently studied classes of graphs (such as bounded degree, degenerated and classes determined by a finite set of for...

Cuts and Bounds

Clopper-Pearson Bounds from HEP Data Cuts

For the measurement of Ns signals in N events rigorous confidence bounds on the true signal probability pexact were established in a classical paper by Clopper and Pearson [Biometrica 26, 404 (1934)]. Here, their bounds are generalized to the HEP situation where cuts on the data tag signals with probability Ps and background data with likelihood Pb < Ps. The Fortran program which, on input of P...

Approximation Bounds for Inference using Cooperative Cuts

We analyze a family of probability distributions that are characterized by an embedded combinatorial structure. This family includes models having arbitrary treewidth and arbitrary sized factors. Unlike general models with such freedom, where the “most probable explanation” (MPE) problem is inapproximable, the combinatorial structure within our model, in particular the indirect use of submodula...

Optimal Lower Bounds for Sketching Graph Cuts

We study the space complexity of sketching cuts and Laplacian quadratic forms of graphs. We show that any data structure which approximately stores the sizes of all cuts in an undirected graph on n vertices up to a 1 + ǫ error must use Ω(n logn/ǫ) bits of space in the worst case, improving the Ω(n/ǫ) bound of [ACK16] and matching the best known upper bound achieved by spectral sparsifiers [BSS1...