79,002 research outputs found
Fast exact algorithms for some connectivity problems parametrized by clique-width
Given a clique-width -expression of a graph , we provide time algorithms for connectivity constraints on locally checkable properties
such as Node-Weighted Steiner Tree, Connected Dominating Set, or Connected
Vertex Cover. We also propose a time algorithm for Feedback
Vertex Set. The best running times for all the considered cases were either
or worse
Infiltration into inclined fibrous sheets
The flow from line and point sources through an inclined fibrous sheet is studied experimentally and theoretically for wicking from a saturated region and flow from a constant-flux source. Wicking from a saturated line generates a wetted region whose length grows diffusively, linearly or tends to a constant, depending on whether the sheet is horizontal or inclined downwards or upwards. A constant-flux line source generates a wetted region which ultimately grows linearly with time, and is characterized by a capillary fringe whose thickness depends on the relative strength of the source, gravitational and capillary forces. Good quantitative agreement is observed between experiments and similarity solutions.Capillary-driven and constant-flux source flows issuing from a point on a horizontal sheet generate a wetted patch whose radius grows diffusively in time. The flow is characterized by the relative strength of the source and spreading induced by the action of capillary forces, gamma. As gamma increases, the fraction of the wetted region which is saturated increases. Wicking from a saturated point corresponds to gamma = gamma(c), and spreads at a slower rate than from a line source. For gamma < gamma(c), the flow is partially saturated everywhere. Good agreement is observed between measured moisture profiles, rates of spreading, and similarity solutions.Numerical solutions are developed for point sources on inclined sheets. The moisture profile is characterized by a steady region circumscribed by a narrow boundary layer across which the moisture content rapidly changes. An approximate analytical solution describes the increase in the size of the wetted region with time and source strength; these conclusions are confirmed by numerical calculations. Experimental measurements of the downslope length are observed to be slightly in excess of theoretical predictions, though the dependence on time, inclination and flow rate obtained theoretically is confirmed. Experimental measurements of cross-slope width are in agreement with numerical results and solutions for short and long times. The affect of a percolation threshold is observed to ultimately arrest cross-slope transport, placing a limitation on the long-time analysis
OBDD-Based Representation of Interval Graphs
A graph can be described by the characteristic function of the
edge set which maps a pair of binary encoded nodes to 1 iff the nodes
are adjacent. Using \emph{Ordered Binary Decision Diagrams} (OBDDs) to store
can lead to a (hopefully) compact representation. Given the OBDD as an
input, symbolic/implicit OBDD-based graph algorithms can solve optimization
problems by mainly using functional operations, e.g. quantification or binary
synthesis. While the OBDD representation size can not be small in general, it
can be provable small for special graph classes and then also lead to fast
algorithms. In this paper, we show that the OBDD size of unit interval graphs
is and the OBDD size of interval graphs is $O(\
| V \ | \log \ | V \ |)\Omega(\ | V \ | \log
\ | V \ |)O(\log \ | V \ |)O(\log^2 \ | V \ |)$ operations and
evaluate the algorithms empirically.Comment: 29 pages, accepted for 39th International Workshop on Graph-Theoretic
Concepts 201
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