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  • 1
    Electronic Resource
    Electronic Resource
    On the complexity of embedding planar graphs to minimize certain distance measures (1990)
    Springer
    Algorithmica 5 (1990), S. 93-109 
    Details
    ISSN: 1432-0541
    Keywords: Planar graphs ; Embedding ; Outer faces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present polynomial-time algorithms for computing an embedding of a planar graph that minimizes the outerplanarity, or the width, or the radius, or some other measures of distance to the outer face. On the other hand, we show it is NP-hard to compute an embedding that minimizes the diameter of the dual graph.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01840379
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A note on the prize collecting traveling salesman problem (1993)
    Springer
    Mathematical programming 59 (1993), S. 413-420 
    Details
    ISSN: 1436-4646
    Keywords: Linear programming ; prize collecting ; rounding fractional solutions ; traveling salesman problem ; worst-case analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We study the version of the prize collecting traveling salesman problem, where the objective is to find a tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertices not in the tour is as small as possible. We present an approximation algorithm with constant bound. The algorithm is based on Christofides' algorithm for the traveling salesman problem as well as a method to round fractional solutions of a linear programming relaxation to integers, feasible for the original problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581256
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    Paper (German National Licenses)
    Fulltext
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