We present an Õ(n)-time algorithm for maintaining the topological order of a directed acyclic graph with n vertices while inserting m edges. This is an improvement over the previous result of O(n) by Ajwani, Friedrich, and Meyer.

We present a simple algorithm which maintains the topological order of a directed acyclic graph with n nodes under an online edge insertion sequence in O(n2.75) time, independent of the number of edges m inserted. For dense DAGs, this is an improvement over the previous best result of O(min{m 3 2 log n,m 32 + n log n}) by Katriel and Bodlaender. We also provide an empirical comparison of our al...

Robertson and Seymour proved that graphs are well-quasi-ordered by the minor relation and the weak immersion relation in the prominent Graph Minors series. That is, given infinitely many graphs, one graph contains another as a minor (or a weak immersion, respectively). However, the topological minor relation does not well-quasi-order graphs. For every positive integer i, let Gi be the graph obt...

A preliminary version of this article appeared in Proceedings of the 35th International Colloquium on Automata, Languages, and Programming (ICALP), Reykjavik, Iceland, July 7-11, 2008. Author’s addresses: Bernhard Haeupler, CSAIL, Massachusetts Institute of Technology, Cambridge, MA 02139, United States, [email protected]; work done while the author was a visiting student at Princeton University...

V. Wessels,1,6,* A. K. Gangopadhyay,1 K. K. Sahu,1,6 R. W. Hyers,2 S. M. Canepari,2 J. R. Rogers,3 M. J. Kramer,4 A. I. Goldman,4 D. Robinson,4,5 J. W. Lee,7 J. R. Morris,7 and K. F. Kelton1 1Washington University, Department of Physics, St. Louis, Missouri 63130, USA 2University of Massachusetts, Department of Mechanical Engineering, Amherst, Massachusetts 01003, USA 3NASA Marshall Space Fligh...

Topological phases - systems with a global ordering in the entanglement exhibit exotic excitations known as anyons which can display highly nontrivial (non-Abelian) statistics. Through transitions between such phases, these undergo rather surprising changes. Perhaps most surprisingly, one anyon split into two or more anyons, some of might condense become confined. The authors propose here compl...

We perform large-scale Monte Carlo simulations of orientational ordering in nematic shells and study the type and position of topological defects when an external electric field (homogeneous or quadrupolar) is applied. The field-induced variation of the defect number (and strength) can be used to change the valence of colloidal particles coated with a nematic layer.

The theory describing quantum smectics in 2+1 dimensions, based on topological quantum melting is presented. This is governed by a dislocation condensate characterized by an ordering of Burger's vector and this "dual shear superconductor" manifests itself in the form of a novel spectrum of phononlike modes.

We report the effect of annealing on crystalline ordering and physical properties in thin films a nodal line semimetal candidate L2 1 -type Co 2 FeSn. The Co–Fe–Sn with composition Co:Fe:Sn ∼ 2:1:1 were deposited MgO(001) substrates at substrate temperature 150 °C by radio-frequency magnetron sputtering. as-deposited film showed x-ray diffraction patterns corresponding to B2 ordering. Annealing...

Hierarchical phrase-based models are attractive because they provide a consistent framework within which to characterize both local and long-distance reorderings, but they also make it dif cult to distinguish many implausible reorderings from those that are linguistically plausible. Rather than appealing to annotationdriven syntactic modeling, we address this problem by observing the in uential...