Branching on multi-aggregated variables

open5siopenGamrath, Gerald; Melchiori, Anna; Berthold, Timo; Gleixner, Ambros M.; Salvagnin, DomenicoGamrath, Gerald; Melchiori, Anna; Berthold, Timo; Gleixner, Ambros M.; Salvagnin, Domenic

Intermediate integer programming representations using value disjunctions

We introduce a general technique to create an extended formulation of a mixed-integer program. We classify the integer variables into blocks, each of which generates a finite set of vector values. The extended formulation is constructed by creating a new binary variable for each generated value. Initial experiments show that the extended formulation can have a more compact complete description than the original formulation. We prove that, using this reformulation technique, the facet description decomposes into one ``linking polyhedron'' per block and the ``aggregated polyhedron''. Each of these polyhedra can be analyzed separately. For the case of identical coefficients in a block, we provide a complete description of the linking polyhedron and a polynomial-time separation algorithm. Applied to the knapsack with a fixed number of distinct coefficients, this theorem provides a complete description in an extended space with a polynomial number of variables.Comment: 26 pages, 5 figure

Digging Deeper for New Physics in the LHC Data

In this paper we describe a novel, model-independent technique of "rectangular aggregations" for mining the LHC data for hints of new physics. A typical (CMS) search now has hundreds of signal regions, which can obscure potentially interesting anomalies. Applying our technique to the two CMS jets+MET SUSY searches, we identify a set of previously overlooked $\sim 3\sigma$ excesses. Among these, four excesses survive tests of inter- and intra-search compatibility, and two are especially interesting: they are largely overlapping between the jets+MET searches and are characterized by low jet multiplicity, zero $b$-jets, and low MET and $H_T$. We find that resonant color-triplet production decaying to a quark plus an invisible particle provides an excellent fit to these two excesses and all other data -- including the ATLAS jets+MET search, which actually sees a correlated excess. We discuss the additional constraints coming from dijet resonance searches, monojet searches and pair production. Based on these results, we believe the wide-spread view that the LHC data contains no interesting excesses is greatly exaggerated.Comment: 31 pages + appendices, 14 figures, source code for recasted searches attached as auxiliary materia