TY - JOUR

T1 - Online interval scheduling on two related machines

T2 - the power of lookahead

AU - Pinson, Nicolas

AU - Spieksma, Frits C.R.

PY - 2019/7/15

Y1 - 2019/7/15

N2 - We consider an online interval scheduling problem on two related machines. If one machine is at least as twice as fast as the other machine, we say the machines are distinct; otherwise the machines are said to be similar. Each job j∈ J is characterized by a length pj, and an arrival time tj; the question is to determine whether there exists a feasible schedule such that each job starts processing at its arrival time. For the case of unit-length jobs, we prove that when the two machines are distinct, there is an amount of lookahead allowing an online algorithm to solve the problem. When the two machines are similar, we show that no finite amount of lookahead is sufficient to solve the problem in an online fashion. We extend these results to jobs having arbitrary lengths, and consider an extension focused on minimizing total waiting time.

AB - We consider an online interval scheduling problem on two related machines. If one machine is at least as twice as fast as the other machine, we say the machines are distinct; otherwise the machines are said to be similar. Each job j∈ J is characterized by a length pj, and an arrival time tj; the question is to determine whether there exists a feasible schedule such that each job starts processing at its arrival time. For the case of unit-length jobs, we prove that when the two machines are distinct, there is an amount of lookahead allowing an online algorithm to solve the problem. When the two machines are similar, we show that no finite amount of lookahead is sufficient to solve the problem in an online fashion. We extend these results to jobs having arbitrary lengths, and consider an extension focused on minimizing total waiting time.

KW - Competitive ratio

KW - Interval scheduling

KW - Lookahead

KW - Online algorithms

UR - http://www.scopus.com/inward/record.url?scp=85059871632&partnerID=8YFLogxK

U2 - 10.1007/s10878-019-00381-6

DO - 10.1007/s10878-019-00381-6

M3 - Article

AN - SCOPUS:85059871632

VL - 38

SP - 224

EP - 253

JO - Journal of Combinatorial Optimization

JF - Journal of Combinatorial Optimization

SN - 1382-6905

IS - 1

ER -