An Asymptotically Optimal Linear-Time Algorithm for Locally Consistent Constraint Satisfaction Problems

2005 ◽  
pp. 603-614
Author(s):  
Daniel Král’ ◽  
Ondřej Pangrác
Keyword(s):  
Constraint Satisfaction ◽  
Linear Time ◽  
Time Algorithm ◽  
Constraint Satisfaction Problems ◽  
Linear Time Algorithm ◽  
Asymptotically Optimal ◽  
Optimal Linear ◽  
Consistent Constraint

scholarly journals A simpler linear-time algorithm for the common refinement of rooted phylogenetic trees on a common leaf set

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
David Schaller ◽  
Marc Hellmuth ◽  
Peter F. Stadler
Keyword(s):  
Phylogenetic Trees ◽  
Linear Time ◽  
Time Algorithm ◽  
Input Tree ◽  
Linear Time Algorithm ◽  
Optimal Algorithms ◽  
Asymptotically Optimal ◽  
The Common ◽  
Mathematical Phylogenetics ◽  
Special Case

Abstract Background The supertree problem, i.e., the task of finding a common refinement of a set of rooted trees is an important topic in mathematical phylogenetics. The special case of a common leaf set L is known to be solvable in linear time. Existing approaches refine one input tree using information of the others and then test whether the results are isomorphic. Results An O(k|L|) algorithm, , for constructing the common refinement T of k input trees with a common leaf set L is proposed that explicitly computes the parent function of T in a bottom-up approach. Conclusion is simpler to implement than other asymptotically optimal algorithms for the problem and outperforms the alternatives in empirical comparisons. Availability An implementation of in Python is freely available at https://github.com/david-schaller/tralda.

MANHATTONIAN PROXIMITY IN A SIMPLE POLYGON

1995 ◽  
Vol 05 (01n02) ◽  
pp. 53-74 ◽  
Author(s):  
ROLF KLEIN ◽  
ANDRZEJ LINGAS
Keyword(s):  
Voronoi Diagram ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Linear Time ◽  
Simple Polygon ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Manhattan Metric ◽  
Optimal Linear ◽  
Planar Polygon

Let P be a simple planar polygon. We present a linear time algorithm for constructing the bounded Voronoi diagram of P in the Manhattan metric, where each point z in P belongs to the region of the closest vertex of P that is visible from z. Among other consequences, the minimum spanning tree of the vertices in the Manhattan metric that is contained in P can be computed within optimal linear time. The same results hold for the L∞-metric.α

scholarly journals An optimal linear time algorithm for quasi-monotonic segmentation1

2009 ◽  
Vol 86 (7) ◽  
pp. 1093-1104 ◽  
Author(s):  
Daniel Lemire ◽  
Martin Brooks ◽  
Yuhong Yan
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Optimal Linear

scholarly journals Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 293
Author(s):  
Xinyue Liu ◽  
Huiqin Jiang ◽  
Pu Wu ◽  
Zehui Shao
Keyword(s):  
Linear Time ◽  
Minimum Weight ◽  
Domination Number ◽  
Time Algorithm ◽  
Simple Graph ◽  
Linear Time Algorithm ◽  
Domination Problem ◽  
Np Complete ◽  
Chordal Bipartite Graphs ◽  
Dominating Function

For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v)≠0 has a neighbor u with f(u)≠0 for every vertex v∈V(G). The weight of a TR3DF f is the sum f(V)=∑v∈V(G)f(v) and the minimum weight of a total Roman {3}-dominating function on G is called the total Roman {3}-domination number denoted by γt{R3}(G). In this paper, we show that the total Roman {3}-domination problem is NP-complete for planar graphs and chordal bipartite graphs. Finally, we present a linear-time algorithm to compute the value of γt{R3} for trees.

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