Scheduling constructive algorithms

For each week of the schedule, every employee must have exactly two days off. In any given week, there are already (IT - n) Sundays off at the beginning of the week and (IT - n) Saturdays off at the end of the week. An additional 2n days must be given off so that all IT people have two days off and the algorithm constructs n off-day pairs for this task. 

FU allocation is based on an EMUCS-like algorithm [5]. Micro-scheduling uses an ASAP algorithm. Component placement and connection allocation make use of improved constructive approaches similar to those used in APOLLON [6]. The originality of the approach is that all of these algorithms are implemented in order to allow mixed manual and automatic design. With the exception of micro-scheduling, they all use a constructive approach. At each step, a new element is allocated or placed. The four steps may be sequenced automatically or performed step by step. Each step may be executed automatically, interactively, or manually. 

Recently, Kothari et al. [56] have proposed a fully polynomial-time approximation scheme (FPTAS) for a variation on this price-schedule problem in which the cost functions are piecewise and marginal-decreasing and each supplier has a capacity constraint. The approach is to construct a 2-approximation to a generalized knapsack problem, which can then be used to scale a dynamicprogramming algorithm and compute an (1 + e) approximation in worst-case time T = 0 nc) /e), for n bidders and with a maximum of c pieces in each bid. ... 

We analyze in this section properties of the algorithms presented in Section 6.3. We prove first the makeWellposed algorithm can minimally serialize an ill-posed constraint graph in attempt to make it well-posed, if a well-posed solution exists. We then prove the iterative incremental scheduling algorithm can construct a minimum relative schedule, if one exists, in polynomial time. 

The iterative incremental scheduling algorithm constructs a minimum relative schedule, or detects the presence of inconsistent timing constraints, with at most i + 1 iterations. This is a very desirable property, since the number of maximum timing constraints i is in general small. The proof follows the outline in [LW83]. Note that in the sequel the full anchor set A(v <) for a valex Vi is used in the computation of the start time and offsets. By Theorem 6.2.4 and Theorem 6.2.6, the result is applicable when the relevant anchor set R vi) or the irredundant anchor set IR(vi) are used instead. 

After the operations within each clusters have been serialized, the clusters are linearly ordered compatible with the original partial order. This linear order can be constructed in linear-time with respect to the number of clusters. The order in which the clusters are visited and resolved is important Therefore, if the above steps fail to find a valid ordering, then this order can be changed and the above steps repeated. By Theorem 6.2.1 and Lemma 6.2.3, a solution to conflict resolution implies that a valid relative schedule exists. In this case, the binding is known to be valid and the iterative incremental scheduling algorithm can be performed to compute the time offsets. 

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