Randomized Speedup of the Bellman-Ford Algorithm

We describe a variant of the Bellman-Ford algorithm for single-source shortest paths in graphs with negative edges but no negative cycles that randomly permutes the vertices and uses this randomized order to process the vertices within each pass of the algorithm. The modification reduces the worst-case expected number of relaxation steps of the algorithm, compared to the previously-best variant by Yen (1970), by a factor of 2/3 with high probability. We also use our high probability bound to add negative cycle detection to the randomized algorithm.Comment: 12 Pages, 6 Figures, ANALCO 201

Crossing Minimization for 1-page and 2-page Drawings of Graphs with Bounded Treewidth

We investigate crossing minimization for 1-page and 2-page book drawings. We show that computing the 1-page crossing number is fixed-parameter tractable with respect to the number of crossings, that testing 2-page planarity is fixed-parameter tractable with respect to treewidth, and that computing the 2-page crossing number is fixed-parameter tractable with respect to the sum of the number of crossings and the treewidth of the input graph. We prove these results via Courcelle's theorem on the fixed-parameter tractability of properties expressible in monadic second order logic for graphs of bounded treewidth.Comment: Graph Drawing 201

Fixed parameter tractability of crossing minimization of almost-trees

We investigate exact crossing minimization for graphs that differ from trees by a small number of additional edges, for several variants of the crossing minimization problem. In particular, we provide fixed parameter tractable algorithms for the 1-page book crossing number, the 2-page book crossing number, and the minimum number of crossed edges in 1-page and 2-page book drawings.Comment: Graph Drawing 201

Criminal neighbourhoods: does the density of prior offenders encourage others to commit crime?

Using crime data over a period of a decade for Glasgow, this paper explores whether the density of prior offenders in a neighbourhoods has an influence on the propensity of others to (re)commence offending. The study shows that the number of ‘newly active’ offenders in a neighbourhood in the current quarter is positively associated with the density of prior offenders for both violent and property crime from the previous two years. In the case of ‘newly active’ property offenders, the relationship with active prior offenders is only apparent when prior offender counts exceed the median. The paper postulates that intraneighbourhood social mechanisms may be at work to create these effects. The results suggest that policies which concentrate offenders in particular neighbourhoods may increase the number of ‘newly active’ offenders, and point to evidence of a threshold at which these effects take place

Pegasus thermal design

Electronic and micrometeoroid detector panels for Pegasus thermal desig

Small Superpatterns for Dominance Drawing

We exploit the connection between dominance drawings of directed acyclic graphs and permutations, in both directions, to provide improved bounds on the size of universal point sets for certain types of dominance drawing and on superpatterns for certain natural classes of permutations. In particular we show that there exist universal point sets for dominance drawings of the Hasse diagrams of width-two partial orders of size O(n^{3/2}), universal point sets for dominance drawings of st-outerplanar graphs of size O(n\log n), and universal point sets for dominance drawings of directed trees of size O(n^2). We show that 321-avoiding permutations have superpatterns of size O(n^{3/2}), riffle permutations (321-, 2143-, and 2413-avoiding permutations) have superpatterns of size O(n), and the concatenations of sequences of riffles and their inverses have superpatterns of size O(n\log n). Our analysis includes a calculation of the leading constants in these bounds.Comment: ANALCO 2014, This version fixes an error in the leading constant of the 321-superpattern siz