ON THE k-TRUCK SCHEDULING PROBLEM

2004 ◽  
Vol 15 (01) ◽  
pp. 127-141 ◽  
Author(s):  
WEIMIN MA ◽  
YINFENG XU ◽  
JANE YOU ◽  
JAMES LIU ◽  
KANLIANG WANG
Keyword(s):  
Lower Bound ◽  
Greedy Algorithm ◽  
Competitive Ratio ◽  
Scheduling Problem ◽  
Competitive Algorithm ◽  
Truck Scheduling ◽  
New Variant ◽  
On Line ◽  
Server Problem ◽  
Better Than

In this paper, some results concerning the k-truck problem are produced. Firstly, the algorithms and their complexity concerning the off-line k-truck problem are discussed. Following that, a lower bound of competitive ratio (1+θ)·k/(θ·k+2) for the on-line k-truck problem is given, where θ is the ratio of cost of the loaded truck and the empty truck on the same distance, and a relevant lower bound for the on-line k-taxi problem followed naturally. Thirdly, based on the Position Maintaining Strategy (PMS), some new results which are slightly better than those of [11] for general cases are obtained. For example, a c-competitive or (c/θ+1/θ+1)-competitive algorithm for the on-line k-truck problem depending on the value of θ, where c is the competitive ratio of some algorithm to a relevant k-server problem, is developed. The Partial-Greedy Algorithm (PG) is used as well to solve this problem on a line with n nodes and is proved to be a (1+(n-k)/θ)-competitive algorithm for this case. Finally, the concepts of the on-line k-truck problem are extended to obtain a new variant: Deeper On-line k-Truck Problem (DTP). We claim that results of PMS for the STP (Standard Truck Problem) hold for the DTP.

A SEMI-ON-LINE SCHEDULING PROBLEM OF TWO PARALLEL MACHINES WITH COMMON MAINTENANCE TIME

2012 ◽  
Vol 29 (04) ◽  
pp. 1250020 ◽  
Author(s):  
YUHUA CAI ◽  
QI FENG ◽  
WENJIE LI
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Parallel Machines ◽  
Time Interval ◽  
Scheduling Problem ◽  
Maintenance Time ◽  
Identical Machines ◽  
On Line

In this paper, we consider a semi-on-line scheduling problem of two identical machines with common maintenance time interval and nonresumable availability. We prove a lower bound of 2.79129 on the competitive ratio and give an on-line algorithm with competitive ratio 2.79633 for this problem.

ONLINE SCHEDULING OF DYNAMIC TREES

1995 ◽  
Vol 05 (04) ◽  
pp. 635-646 ◽  
Author(s):  
MICHAEL A. PALIS ◽  
JING-CHIOU LIOU ◽  
SANGUTHEVAR RAJASEKARAN ◽  
SUNIL SHENDE ◽  
DAVID S.L. WEI
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Scheduling Algorithm ◽  
Optimal Schedule ◽  
Online Scheduling ◽  
The Other ◽  
Static Case ◽  
Scheduling Problem ◽  
Dynamic Trees ◽  
Dynamic Tree

The scheduling problem for dynamic tree-structured task graphs is studied and is shown to be inherently more difficult than the static case. It is shown that any online scheduling algorithm, deterministic or randomized, has competitive ratio Ω((1/g)/ log d(1/g)) for trees with granularity g and degree at most d. On the other hand, it is known that static trees with arbitrary granularity can be scheduled to within twice the optimal schedule. It is also shown that the lower bound is tight: there is a deterministic online tree scheduling algorithm that has competitive ratio O((1/g)/ log d(1/g)). Thus, randomization does not help.

scholarly journals On-line Search in Two-Dimensional Environment

2019 ◽  
Vol 63 (8) ◽  
pp. 1819-1848
Author(s):  
Dariusz Dereniowski ◽  
Dorota Osula
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Mobile Agents ◽  
Line Search ◽  
Search Strategy ◽  
A Priori ◽  
Two Dimensional ◽  
Pursuit Evasion ◽  
On Line ◽  
Evasion Problem

Abstract We consider the following on-line pursuit-evasion problem. A team of mobile agents called searchers starts at an arbitrary node of an unknown network. Their goal is to execute a search strategy that guarantees capturing a fast and invisible intruder regardless of its movements using as few searchers as possible. We require that the strategy is connected and monotone, that is, at each point of the execution the part of the graph that is guaranteed to be free of the fugitive is connected and whenever some node gains a property that it cannot be occupied by the fugitive, the strategy must operate in such a way to keep this property till its end. As a way of modeling two-dimensional shapes, we restrict our attention to networks that are embedded into partial grids: nodes are placed on the plane at integer coordinates and only nodes at distance one can be adjacent. Agents do not have any knowledge about the graph a priori, but they recognize the direction of the incident edge (up, down, left or right). We give an on-line algorithm for the searchers that allows them to compute a connected and monotone strategy that guarantees searching any unknown partial grid with the use of $O(\sqrt {n})$ O ( n ) searchers, where n is the number of nodes in the grid. As for a lower bound, there exist partial grids that require ${\varOmega }(\sqrt {n})$ Ω ( n ) searchers. Moreover, we prove that for each on-line searching algorithm there is a partial grid that forces the algorithm to use ${\varOmega }(\sqrt {n})$ Ω ( n ) searchers but $O(\log n)$ O ( log n ) searchers are sufficient in the off-line scenario. This gives a lower bound on ${\varOmega }(\sqrt {n}/\log n)$ Ω ( n / log n ) in terms of achievable competitive ratio of any on-line algorithm.

ON THE LOWER BOUND OF THE COMPETITIVE RATIO FOR THE WEIGHTED ONLINE ROOMMATES PROBLEM

2010 ◽  
Vol 02 (02) ◽  
pp. 257-262
Author(s):  
SATYAJIT BANERJEE
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Deterministic Algorithm ◽  
Weighted Version ◽  
Worst Case ◽  
Competitive Algorithm

We show that the best possible worst case competitive ratio of any deterministic algorithm for weighted online roommates problem is arbitrarily close to 4. This proves that the 4-competitive algorithm proposed by Bernstein and Rajagopalan [3] for the weighted version of the online roommates problem actually attains the best possible competitive ratio.

SEMI-ON-LINE SCHEDULING PROBLEM FOR MAXIMIZING THE MINIMUM MACHINE COMPLETION TIME ON THREE SPECIAL UNIFORM MACHINES

2005 ◽  
Vol 22 (02) ◽  
pp. 229-237 ◽  
Author(s):  
RUN-ZI LUO ◽  
SHI-JIE SUN
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Processing Time ◽  
Scheduling Problem ◽  
Uniform Machines ◽  
On Line ◽  
Special Case

In this paper, we investigate a semi-on-line version for a special case of three machines M1, M2, M3 where the processing time of the largest job is known in advance. A speed si(s1 = s2 = 1, 1 ≤ s3 = s) is associated with machine Mi. Our goal is to maximize the C min — the minimum workload of three machines. We give a C min 3 algorithm and prove its competitive ratio is [Formula: see text] and the algorithm is the best possible for 1 ≤ s ≤ 2. We also claim the competitive ratio of algorithm C min 3 is tight.

LOWER BOUNDS FOR STREETS AND GENERALIZED STREETS

2001 ◽  
Vol 11 (04) ◽  
pp. 401-421 ◽  
Author(s):  
ALEJANDRO LÓPEZ-ORTIZ ◽  
SVEN SCHUIERER
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Real Line ◽  
Upper Bound ◽  
Competitive Ratio ◽  
Search Strategy ◽  
The Real ◽  
Simple Polygons ◽  
On Line ◽  
Special Classes

We present lower bounds for on-line searching problems in two special classes of simple polygons called streets and generalized streets. In streets we assume that the location of the target is known to the robot in advance and prove a lower bound of [Formula: see text] on the competitive ratio of any deterministic search strategy—which can be shown to be tight. For generalized streets we show that if the location of the target is not known, then there is a class of orthogonal generalized streets for which the competitive ratio of any search strategy is at least [Formula: see text] in the L2-metric—again matching the competitive ratio of the best known algorithm. We also show that if the location of the target is known, then the competitive ratio for searching in generalized streets in the L1-metric is at least 9 which is tight as well. The former result is based on a lower bound on the average competitive ratio of searching on the real line if an upper bound of D to the target is given. We show that in this case the average competitive ratio is at least 9-O(1/ log D).

Developing a lower bound and strong heuristics for a truck scheduling problem in a cross-docking center

2017 ◽  
Vol 129 ◽  
pp. 17-38 ◽  
Author(s):  
Amir Golshahi-Roudbaneh ◽  
Mostafa Hajiaghaei-Keshteli ◽  
Mohammad Mahdi Paydar
Keyword(s):  
Lower Bound ◽  
Scheduling Problem ◽  
Cross Docking ◽  
Truck Scheduling

A better lower bound on the competitive ratio of the randomized 2-server problem

1997 ◽  
Vol 63 (2) ◽  
pp. 79-83 ◽  
Author(s):  
Marek Chrobak ◽  
Lawrence L. Larmore ◽  
Carsten Lund ◽  
Nick Reingold
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Server Problem

ONLINE SCHEDULING OF MIXED CPU-GPU JOBS

2014 ◽  
Vol 25 (06) ◽  
pp. 745-761 ◽  
Author(s):  
LIN CHEN ◽  
DESHI YE ◽  
GUOCHUAN ZHANG
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Online Algorithm ◽  
Online Scheduling ◽  
Scheduling Problem ◽  
Competitive Algorithm ◽  
Processing Times ◽  
Special Cases ◽  
Identical Machines ◽  
The One

We consider the online scheduling problem in a CPU-GPU cluster. In this problem there are two sets of processors, the CPU processors and the GPU processors. Each job has two distinct processing times, one for the CPU processor and the other for the GPU processor. Once a job is released, a decision should be made immediately about which processor it should be assigned to. The goal is to minimize the makespan, i.e., the largest completion time among all the processors. Such a problem could be seen as an intermediate model between the scheduling problem on identical machines and unrelated machines. We provide a 3.85-competitive online algorithm for this problem and show that no online algorithm exists with competitive ratio strictly less than 2. We also consider two special cases of this problem, the balanced case where the number of CPU processors equals to that of GPU processors, and the one-sided case where there is only one CPU or GPU processor. For the balanced case, we first provide a simple 3-competitive algorithm, and then a better algorithm with competitive ratio of 2.732 is derived. For the one-sided case, a 3-competitive algorithm is given.

ONLINE ALGORITHMS FOR SCHEDULING WITH MACHINE ACTIVATION COST

2007 ◽  
Vol 24 (02) ◽  
pp. 263-277 ◽  
Author(s):  
YONG HE ◽  
SHUGUANG HAN ◽  
YIWEI JIANG
Keyword(s):  
Lower Bound ◽  
Online Algorithms ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Scheduling Problem ◽  
Identical Machines ◽  
Parallel Machine Scheduling Problem

In this paper, we consider a variant of the classical parallel machine scheduling problem. For this problem, we are given m potential identical machines to non-preemptively process a sequence of independent jobs. Machines need to be activated before starting to process, and each machine activated incurs a fixed machine activation cost. No machines are initially activated, and when a job is revealed the algorithm has the option to activate new machines. The objective is to minimize the sum of the makespan and activation cost of machines. We first present two optimal online algorithms with competitive ratios of 3/2 and 5/3 for m = 2, 3 cases, respectively. Then we present an online algorithm with a competitive ratio of at most 2 for general m ≥ 4, while the lower bound is 1.88.

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