Plotkin, Rao, and Smith (SODA’97) showed that any graph with m edges and n vertices that excludes Kh as a depth O(l logn)-minor has a separator of size O(n/l + lh logn) and that such a separator can be found in O(mn/l) time. A time bound of O(m + n/l) for any constant ǫ > 0 was later given (W., FOCS’11) which is an improvement for non-sparse graphs. We give three new algorithms. The first has t...

A set of vertices S ⊆ V is called a safe separator for treewidth, if S is a separator of G, and the treewidth of G equals the maximum of the treewidth over all connected components W of G S of the graph, obtained by making S a clique in the subgraph of G, induced by W ∪ S. We show tha t such safe separators are a very powerful tool for preprocessing graphs when we want to compute their treewidt...

Given an n-vertex weighted planar graph G, a separator is a subset S of vertices such that each component of G S has at most two-thirds of the original weight. We give an algorithm nding a separator while balancing these two parameters of G[S]: the number of components, and the cost of a minimum spanning forest. In particular, given uniform edge costs and a positive integer k pn, we nd a separa...

We introduce the concept of multi-directional width-bounded geometric separators and obtain an improved separator for grid graphs. This yields an improved exact algorithm for the protein folding problem in the HP-model. For a grid graph G with n grid points P , there exists a separator A ⊆ P such that A has at most 1.02074 √ n points, and G−A has two disconnected subgraphs each with at most 2 3...

grammar ThreeFieldGrammar; structure { start: field1 & separator & field2 & separator & field3 & "\n"; separator: "-"; abstract field1; abstract field2; abstract field3; } An abstract grammar captures an incomplete specification. A non-terminal node must be declared abstract if it does not have a corresponding RHS. A grammar that has at least one abstract node must be declared abstract. A deriv...

A separator for two languages is a third language containing the first one and disjoint from the second one. We investigate the following decision problem: given two regular input languages, decide whether there exists a locally testable (resp. a locally threshold testable) separator. In both cases, we design a decision procedure based on the occurrence of special patterns in automata accepting...

BACKGROUND This study aims to evaluate and compare the effect of pre-procedural administration of acetaminophen, ibuprofen, and meloxicam in reducing pain after separator placement. METHODS Three hundred twenty-one patients who needed orthodontic treatment and aged above 15 were randomly assigned to one of the three study groups: group A: 650 mg acetaminophen, group B: 400 mg ibuprofen, and g...

The Vertex Separator Problem for a graph is to find the smallest collection of vertices whose removal breaks the graph into two disconnected subsets that satisfy specified size constraints. The Vertex Separator Problem was formulated in the paper 10.1016/j.ejor.2014.05.042 as a continuous (non-concave/non-convex) bilinear quadratic program. In this paper, we develop a more general continuous bi...

We present a system of interrelated conjectures which can be considered as restricted addition counterparts of classical theorems due to Kneser, Kemperman, and Scherk. Connections with the theorem of Cauchy-Davenport, conjecture of ErdősHeilbronn, and polynomial method of Alon-Nathanson-Ruzsa are discussed. The paper assumes no expertise from the reader and can serve as an introduction to the s...

We study separating equilibria (SE) in pure signaling games in which both type and signaling spaces aremultidimensional, the sender payoff is quasi-linear and receiver utility is independent of the signal (pure signaling case). We show for a large class of cost functions that a sender’s strategy constitutes an SE if and only if it satisfies a certain set of conditions. In particular, we show th...