Linear time algorithms on circular-arc graphs
Information Processing Letters
Chromatic nearest neighbor searching: a query sensitive approach
Computational Geometry: Theory and Applications
Disjoint paths in circular arc graphs
Nordic Journal of Computing
Smallest Color-Spanning Objects
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Finding an optimal path without growing the tree
Journal of Algorithms
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
A PTAS for TSP with neighborhoods among fat regions in the plane
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On intersecting a set of parallel line segments with a convex polygon of minimum area
Information Processing Letters
TSP with neighborhoods of varying size
Journal of Algorithms
Computing minimum diameter color-spanning sets
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
NP-completeness of spreading colored points
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Computing toolpaths for 5-axis NC machines
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Recognition of minimum width color-spanning corridor and minimum area color-spanning rectangle
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
Approximation algorithms for euclidean group TSP
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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We present new algorithms for two problems on interval structures that arise in computer-aided manufacturing and in other areas. We give an O(Kn) time algorithm for the single-source K-link shortest path problem on an interval graph with n weighted vertices, and two O(n) time algorithms for a generalized version of the optimal colorspanning problem for n points on a real line, where each point is assigned one of m colors (m ≤ n). A standard approach for solving the K-link shortest path problem would take O(Kn2) time, and thus our result offers a linear time improvement. The previously best known algorithm for the optimal color-spanning problem in R1 takes O(n) time and space. We provide two algorithms for a generalized version of this problem in which each color must appear a specified minimum number of times. One of these two solutions is suitable for an online processing of the (streaming) input points; it uses O(m) working space for the ordinary 1-D optimal color-spanning problem.