L. Finta, Z. Liu, "Single Machine Scheduling Subject to Precedence Delays", Rapport de Recherche INRIA, No. 2198, 1994. submitted.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... 1g) r i jLmax P jp i = 1; int order(mono l ij ) r i jLmax P2jp i = 1; prec(l ij 2 f1; 0g) r i jLmax 1jp i 1; prec(l ij 2 f0; 1g)jCmax Palem [33] Palem and Simons [34] 1jp i = 1; prec(l ij 2 f0; 1g)jLmax P jp i = 1; int order(mono l ij )jLmax P2jp i = 1; prec; r i jLmax Finta and Liu [10] 1jp i 1; prec(l ij = 1)jCmax Bruno, Jones, So [8] 1jp i = 1; prec(l ij = 1) r i jLmax P jp i = 1; intree(l ij = l)jLmax P jp i = 1; outtree(l ij = l) r i jCmax P jp i = 1; tree(l ij = l)jCmax Hu [23] P jp i = p; treejCmax P2jp i = 1; precjLmax Bernstein and Gertner [5] 1jp i = 1; ....

....and deadlines. The algorithm for this case is due to an early result by Garey and Johnson [14] which runs in O(n ) time. Ignoring both release times and deadlines and considering only the makespan minimization case, 1) We can generalize one of the recent results due to Finta and Liu [10] and show that modi ed deadlines computed with our algorithm can be used with list scheduling to minimize the makespan on one processor with arbitrary precedence constraints, individual processing times p i 1 and zero or unit latencies; the work in [10] proves this fact for unit latencies ....

[Article contains additional citation context not shown here]

Finta, L., and Liu, Z. Single machine scheduling subject to precedence delays. Discrete Applied Mathematics 70 (1996), 247-266.

....some other RISC machines such as IBM RISC System 6000 [24] the maximum latency is more than one cycle. Latencies complicate instruction scheduling. The general problem for scheduling instructions in a basic block so that the maximum completion time is minimized is NP complete even on one processor [9, 8] if the latencies can be arbitrarily large. For bounded latencies and one processor, the complexity status of instruction scheduling is still open. However, the following special cases have been shown to be solvable in polynomial time. 1. Arbitrary DAG (Directed Acyclic Graph) latencies in f0; ....

....be arbitrarily large. For bounded latencies and one processor, the complexity status of instruction scheduling is still open. However, the following special cases have been shown to be solvable in polynomial time. 1. Arbitrary DAG (Directed Acyclic Graph) latencies in f0; 1g and one processor [5, 8]. 2. in forest or out forest, equal latencies and multiple processors [7, 6] 3. Monotone interval graph and multiple processors [1] In real time systems such as flight control systems, computation is subject to timing constraints. Typical timing constraints are in the form of deadlines. The ....

Finta, L. and Z. Liu. Single machine scheduling subject to precedence delays. Discrete Applied Mathematics 70, 247-266, 1996.

....algorithms: precedence delays. Precedence delays have been used to model single processor latencies that arise due to pipelined architectures. Bernstein and Gertner [1] use a modification of the Coffman Graham algorithm [3] to solve 1 j prec; p j = 1; l i; j 2 f0;1g j C max . 2 Finta and Liu [5] give a polynomial time algorithm for the more general 1 j prec; p j ; l i; j 2 f0;1g j C max . Both of these algorithms crucially depend on assuming unit delays between jobs. Polynomial algorithms: communication delays. In the classical models of parallel computation, communication delays are ....

Lucian Finta and Zhen Liu. Single machine scheduling subject to precedence delays. DAMATH: Discrete Applied Mathematics and Combinatorial Operations Research and Computer Science, 70, 1996.

....release times and deadlines and considering the makespan minimization case, 1 The algorithm can use space that is proportional to the difference between the values of the largest of all deadlines, and the smallest of all release times. 1. We can generalize the recent result due to Finta and Liu [5] and show that modified deadlines computed with our algorithm can be used with list scheduling to minimize the makespan of a schedule on one processor with arbitrary precedence constraints, individual processing times p i 1 and zero or unit latencies; the work in [5] proves this fact for unit ....

.... result due to Finta and Liu [5] and show that modified deadlines computed with our algorithm can be used with list scheduling to minimize the makespan of a schedule on one processor with arbitrary precedence constraints, individual processing times p i 1 and zero or unit latencies; the work in [5] proves this fact for unit latencies only. 2. Our algorithm specializes to most of the previously known cases such as the classical two processor scheduling due to Coffman and Graham [4] again via the unification in [15] 4. Computing the Modified Deadlines The modified deadlines computation ....

[Article contains additional citation context not shown here]

L. Finta and Z. Liu. Single machine scheduling subject to precedence delays. Discrete Applied Mathematics, 70:247-- 266, 1996.

.... l ij ) r i Lmax P2 p i = 1; prec(l ij # 1, 0 ) r i Lmax 1 p i # 1; prec(l ij # 0, 1 ) Cmax Palem [28] Palem and Simons [29] 1 p i = 1; prec(l ij # 0, 1 ) Lmax P p i = 1; int order(mono l ij ) Lmax Garey and Johnson [10] P2 p i = 1; prec; r i Lmax Finta and Liu [6] 1 p i # 1; prec(l ij = 1) Cmax Bruno, Jones, So [4] 1 p i = 1; prec(l ij = 1) r i Lmax P p i = 1; intree(l ij = l) Lmax P p i = 1; outtree(l ij = l) r i Cmax P p i = 1; tree(l ij = l) Cmax Hu [18] P p i = p; tree Cmax Garey and Johnson [9] P2 p i = 1; prec Lmax ....

....and deadlines. The algorithm for this case is due to an early result by Garey and Johnson [10] which runs in O(n 3 ) time. Ignoring both release times and deadlines and considering only the makespan minimization case, 1) We can generalize one of the recent results due to Finta and Liu [6] and show that modified deadlines computed with our algorithm can be used with list 8 Leung, Palem and Pnueli TCPS Hennessy and Gross [16] 1 p i = 1; prec(l ij ) Cmax Palem and Simons [29] 1 p i = 1; chains(l ij # 0, k1 , k2 ) Cmax Garey and Johnson [11] P p i = 1; prec Cmax P ....

[Article contains additional citation context not shown here]

Finta, L., and Liu, Z. Single machine scheduling subject to precedence delays. Discrete Applied Mathematics 70 (1996), 247--266.

....other RISC machines such as IBM RISC System 6000 [22] the maximum latency is more than one cycle. Latencies complicate instruction scheduling. The general problem for scheduling instructions in a basic block so that the maximum completion time is minimized is NP complete even on single processor [8, 7] if the latencies can be arbitrary large integer. For bounded latencies and single processor, the complexity status of instruction scheduling is still open. The following special classes are solvable in polynomial time. 1. Arbitrary DAG(Directed Acyclic Graph) latencies in f0; 1g and one ....

....the latencies can be arbitrary large integer. For bounded latencies and single processor, the complexity status of instruction scheduling is still open. The following special classes are solvable in polynomial time. 1. Arbitrary DAG(Directed Acyclic Graph) latencies in f0; 1g and one processor [4, 7]. 2. in tree or out forest , identical latencies and multiple processors[6, 5] 3. Monotone interval graph and multiple processors[1] Palem and Simon[1] proposed an approximation algorithm for scheduling instructions in a basic block with deadlines on multiple RISC machines where latencies are ....

Finta, L. and Z. Liu. Single machine scheduling subject to precedence delays. Discrete Applied Mathematics 70, 247-266, 1996.

....and deadlines and considering the makespan minimization case, 1 The algorithm can use space that is proportional to the difference between the values of the largest of all deadlines, and the smallest of all release times. 1. We can generalize the recent result due to Finta and Liu [5] and show that modified deadlines computed with our algorithm can be used with list scheduling to minimize the makespan of a schedule on one processor with arbitrary precedence constraints, individual processing times p i 1 and zero or unit latencies; the work in [5] proves this fact for unit ....

.... result due to Finta and Liu [5] and show that modified deadlines computed with our algorithm can be used with list scheduling to minimize the makespan of a schedule on one processor with arbitrary precedence constraints, individual processing times p i 1 and zero or unit latencies; the work in [5] proves this fact for unit latencies only. 2. Our algorithm specializes to most of the previously known cases such as the classical two processor scheduling due to Coffman and Graham [4] again via the unification in [15] 4. Computing the Modified Deadlines The modified deadlines computation ....

[Article contains additional citation context not shown here]

L. Finta and Z. Liu. Single machine scheduling subject to precedence delays. Discrete Applied Mathematics, 70:247-- 266, 1996.

....problems that were open before is clarified. 1. Introduction Recent papers devoted to unit time flow shop, open shop and job shop scheduling problems represent polynomial time reductions from these problems to problems on identical parallel machines. Schaffer and Simons [SS88] Finta and Liu [FL96], Brucker and Knust [BK98] consider reductions of nonpreemptive unit time flow shop problems to preemptive arbitrary time or nonpreemptive unit time problems on identical parallel machines. Liu and Bulfin [LB88] Brucker, Jurisch and Jurisch [BJJ93] Braesel, Kluge and Werner [BKW95] describe ....

.... 1jC max [BJS80] P jouttree; p j = 1j SigmaC j [H61] Ojouttree; p j = 1j SigmaC j [BKW95] F jouttree; p ij = 1j SigmaC j [BK98] P2jprec; p j = 1j Cmax SigmaC j [FKN69] CG72] S76] G82] CG72] O2jtree; p j = 1j SigmaC j [BKW95] F2jprec; p ij = 1j Cmax SigmaC j [BJS80] SS88] HMS88] [FL96] [BK98] is n. But the problem size of the chain like precedence constrained special cases is h when own compact encoding. In application to these cases polynomial time algorithms known for the tree like or general precedence constrained problems remain polynomial in n, hence, they are exponential ....

L. Finta and Z. Liu, Single machine scheduling subject to precedence delays, Discrete Appl. Math. 70 (1996), 247--266.

.... after the completion of job i (minimal time lag) On the other hand, if l ij 0 holds, job j cannot start earlier than jl ij j time units before the finishing time of job i (maximal time lag) Complexity results for scheduling problems with time lags have been obtained by Wikum et al. 1994] and Finta Liu [1996]. In Brucker et al. 1997] it has been shown that most of the classical scheduling problems can be polynomially reduced to single machine problems with time lags. We consider single machine problems with time lags l ij = l 0 which means that we only have generalized precedences of the form C i ....

....it is polynomially solvable by the same algorithm which solves 1 j p j = 1; prec (l = 1) j C max . Problem 1 j p j = 1; prec (l = 1) j C max is equivalent to the bump number problem which has independently been solved by Sch affer Simons [1988] and Habib et al. 1988] Sch affer Simons and Finta Liu [1996] showed that the algorithm from Coffman Graham [1972] for the parallel machine problem P2 j p j = 1; prec j C max also solves the single machine problems 1 j p j = 1; prec (l = 1) j C max and 1 j prec (l = 1) j C max , respectively. This algorithm numbers the jobs j = 1; n iteratively ....

[Article contains additional citation context not shown here]

Finta, L., Liu. Z. [1996] Single machine scheduling subject to precedence delays, Discrete Applied Mathematics 70, 247-266.

....oe : V f0; 1; 2; Delta Delta Delta ; T Gamma 1g such that oe(i) 1 l ij oe(j) and r j oe(j) T Gamma d j Gamma 1 for all (i; j) 2 E Lemma 2 The single machine problem (P1) is NP complete. Proof. The proof is analogous to (although slightly more involved than) that in Finta and Liu [3]. A detailed proof is given in Appendix A. Lemma 3 Problem (P1) polynomially transforms to (PR2) RR n2302 16 L. Finta, Z. Liu Proof. Given an instance graph e G = e V ; e E) 2 e G of problem (P1) we construct an instance graph G = V; E) for problem (PR2) As we mentioned ....

....Thus, the NP hardness of analyzed problems extends of course to scheduling problems with general communication semantics and communication mechanisms. It is easily seen that our results applies also to multiprocessor systems with shared memory. Appendices A Proof of Lemma 3 As discussed in [3], the release times and delivery times have no effect on the complexity of problem (P1) Indeed, it suffices to add a fictitious initial task and a fictitious final task in the task graph such that all tasks are successors of the fictitious initial task and predecessors of the fictitious final ....

L. Finta, Z. Liu, "Single Machine Scheduling Subject to Precedence Delays", Rapport de Recherche INRIA, No. 2198, 1994. submitted. RR n2302 42 L. Finta, Z. Liu

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L. Finta, Z. Liu, "Single Machine Scheduling Subject to Precedence Delays", Rapport de Recherche INRIA, No. 2198, 1994. submitted.

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Finta, L. and Liu, Z. (1996). Single Machine Scheduling Subject to Precedence Delays, Discrete Applied Mathematics, 70, 247-266.

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Finta, L. and Z. Liu. Single machine scheduling subject to precedence delays. Discrete Applied Mathematics 70, 1996, 247-266.

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L. Finta and Z. Liu. Single Machine Scheduling Subject to Precedence Delays. RR-2198, INRIA, 1994.

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L. Finta and Z. Liu. Single Machine Scheduling Subject to Precedence Delays. RR-2198, INRIA, 1994.

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