The jump number problem on interval orders: A 32 approximation algorithm
نویسندگان
چکیده
منابع مشابه
A 3/2-Approximation Algorithm for the Jump Number of Interval Orders
The jump number of a partial order P is the minimum number of incomparable adjacent pairs in some linear extension of P. The jump number problem is known to be NP {hard in general. However some particular classes of posets admit easy calculation of the jump number. The complexity status for interval orders still remains unknown. Here we present a heuristic that, given an interval order P , gene...
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15 صفحه اولComputing the Jump Number on Semi-orders Is Polynomial
1) Introduction and notations In this first section we will give our main definitions and recall different characterizations of interval and semi-orders. In section 2 we shall prove that after a decomposition routine, semi-orders have at most 2 consecutive bumps in a linear extension. We also prove, using a "divide-and-conquer" argument, that computing polynomially the jump number can be done p...
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The problems of scheduling jobs on a single machine subject to precedence constraints can often be modelled as the jump number problem for posets, where a linear extension of a given partial order is to be found which minimizes the number of noncomparabilities. In this paper, we are investigating a restricted class of posets, called interval orders, admitting approximation algorithms for the ju...
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First, Cogis and Habib (RAIRO Inform. 7Mor. 13 (1979), 3-18) solved the jump number problem for series-parallel partially ordered sets (posets) by applying the greedy algorithm and then Rival (Proc. Amer. Math. Sot. 89 (1983). 387-394) extended their result to N-free posets. The author (Order 1 (1984), 7-19) provided an interpretation of the latter result in the terms of arc diagrams of posets ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1995
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00290-y