New Upper Bounds for Equiangular Lines by Pillar Decomposition

New Bounds for Equiangular Lines and Spherical Two-Distance Sets

The set of points in a metric space is called an s-distance set if pairwise distances between these points admit only s distinct values. Two-distance spherical sets with the set of scalar products {α,−α}, α ∈ [0, 1), are called equiangular. The problem of determining the maximal size of s-distance sets in various spaces has a long history in mathematics. We determine a new method of bounding th...

Bounds on Equiangular Lines and on Related Spherical Codes

An L-spherical code is a set of Euclidean unit vectors whose pairwise inner products belong to the set L. We show, for a fixed α, β > 0, that the size of any [−1,−β] ∪ {α}-spherical code is at most linear in the dimension. In particular, this bound applies to sets of lines such that every two are at a fixed angle to each another.

Equiangular lines in Euclidean spaces

New Upper Bounds for Maximum -

We develop and experiment with new upper bounds for the constrained maximum-entropy sampling problem. Our partition bounds are based on Fischer's inequality. Further new upper bounds combine the use of Fischer's inequality with previously developed bounds. We demonstrate this in detail by using the partitioning idea to strengthen the spectral bounds of Ko, Lee and Queyranne and of Lee. Computat...

New Upper Bounds for MaxSat

We describe exact algorithms that provide new upper bounds for the Maximum Satisfiability problem (MaxSat). We prove that MaxSat can be solved in time O(|F | · 1.3972), where |F | is the length of a formula F in conjunctive normal form and K is the number of clauses in F . We also prove the time bounds O(|F | · 1.3995), where k is the maximum number of satisfiable clauses, and O((1.1279) ) for ...