TY - CHAP

T1 - Job Shop Scheduling with Unit Length Tasks

T2 - Bounds and Algorithms

AU - Hromkovic, Juraj

AU - Steinhofel, Kathleen

AU - Widmayer, Peter

PY - 2001

Y1 - 2001

N2 - We consider the job shop scheduling problem unit-J m, where each job is processed once on each of m given machines. The execution of any task on its corresponding machine takes exactly one time unit. The objective is to minimize the overall completion time, called makespan. The contribution of this paper are the following results: (i) For any input instance of unit-J m with d jobs, the makespan of an optimum schedule is at most m+o(m), for d = o(m 1/2). For d = o(m 1/2), this improves on the upper bound O(m+d) given in [LMR99] with a constant equal to two as shown in [S98]. For d = 2 the upper bound is improved to m+|√m| . (ii) There exist input instances of unit-J m with d = 2 such that the makespan of an optimum schedule is at least m+|√m| , i.e., the result (i) cannot be improved for d = 2. (iii) We present a randomized on-line approximation algorithm for unit-J m with the best known approximation ratio for d = o(m 1/2). (iv) A deterministic approximation algorizhm for unit-J m is described that works in quadratic time for constant d and has an approximation ratio of 1+2d/⌊√m⌋ for d ≤ 2 log2 m.

AB - We consider the job shop scheduling problem unit-J m, where each job is processed once on each of m given machines. The execution of any task on its corresponding machine takes exactly one time unit. The objective is to minimize the overall completion time, called makespan. The contribution of this paper are the following results: (i) For any input instance of unit-J m with d jobs, the makespan of an optimum schedule is at most m+o(m), for d = o(m 1/2). For d = o(m 1/2), this improves on the upper bound O(m+d) given in [LMR99] with a constant equal to two as shown in [S98]. For d = 2 the upper bound is improved to m+|√m| . (ii) There exist input instances of unit-J m with d = 2 such that the makespan of an optimum schedule is at least m+|√m| , i.e., the result (i) cannot be improved for d = 2. (iii) We present a randomized on-line approximation algorithm for unit-J m with the best known approximation ratio for d = o(m 1/2). (iv) A deterministic approximation algorizhm for unit-J m is described that works in quadratic time for constant d and has an approximation ratio of 1+2d/⌊√m⌋ for d ≤ 2 log2 m.

U2 - 10.1007/3-540-45446-2_6

DO - 10.1007/3-540-45446-2_6

M3 - Conference paper

SN - 9783540426721

VL - N/A

T3 - Lecture Notes in Computer Science

SP - 90

EP - 106

BT - Theoretical Computer Science

A2 - Restivo, Antonio

A2 - Roversi, Luca

A2 - Ronchi Della Rocca, S

PB - Springer Finance

CY - Berlin ; London ; New York

ER -