An improved approximation ratio for the jump number problem on interval orders
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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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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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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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2013
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2013.10.011