Despite more than a decade of experimental work in multi-robot systems, important theoretical aspects of multi-robot coordination mechanisms have, to date, been largely untreated. To address this issue, we focus on the problem of multi-robot task allocation (MRTA). Most work on MRTA has been ad hoc and empirical, with many coordination architectures having been proposed and validated in a proof-of-concept fashion, but infrequently analyzed. With the goal of bringing objective grounding to this important area of research, we present a formal study of MRTA problems. A domain-independent taxonomy of MRTA problems is given, and it is shown how many such problems can be viewed as instances of other, well-studied, optimization problems. We demonstrate how relevant theory from operations research and combinatorial optimization can be used for analysis and greater understanding of existing approaches to task allocation, and show how the same theory can be used in the synthesis of new approaches.

/pdf/a-formal-analysis-and-taxonomy-of-task-allocation-in-multi-37udlnz144.pdf

A Formal Analysis and Taxonomy of Task Allocation in Multi-Robot Systems

Static scheduling of a program represented by a directed task graph on a multiprocessor system to minimize the program completion time is a well-known problem in parallel processing. Since finding an optimal schedule is an NP-complete problem in general, researchers have resorted to devising efficient heuristics. A plethora of heuristics have been proposed based on a wide spectrum of techniques, including branch-and-bound, integer-programming, searching, graph-theory, randomization, genetic algorithms, and evolutionary methods. The objective of this survey is to describe various scheduling algorithms and their functionalities in a contrasting fashion as well as examine their relative merits in terms of performance and time-complexity. Since these algorithms are based on diverse assumptions, they differ in their functionalities, and hence are difficult to describe in a unified context. We propose a taxonomy that classifies these algorithms into different categories. We consider 27 scheduling algorithms, with each algorithm explained through an easy-to-understand description followed by an illustrative example to demonstrate its operation. We also outline some of the novel and promising optimization approaches and current research trends in the area. Finally, we give an overview of the software tools that provide scheduling/mapping functionalities.

http://charm.cs.uiuc.edu/users/arya/docs/6.pdf

Static scheduling algorithms for allocating directed task graphs to multiprocessors

Complexity and Approximation

http://www.upv.es/deioac/Investigacion/revision.pdf

The hybrid flow shop scheduling problem

In many applications involving make-to-order or time-sensitive (e.g., perishable, seasonal) products, finished orders are often delivered to customers immediately or shortly after the production. Consequently, there is little or no finished product inventory in the supply chain such that production and outbound distribution are very intimately linked and must be scheduled jointly to achieve a desired on-time delivery performance at minimum total cost. Research on integrated scheduling models of production and outbound distribution is relatively recent but is growing very rapidly. In this paper, we provide a survey of such existing models. We present a unified model representation scheme, classify existing models into several different classes, and for each class of the models give an overview of the optimality properties, computational tractability, and solution algorithms for the various problems studied in the literature. We clarify the tractability of some open problems left in the literature and some new problems by providing intractability proofs or polynomial-time exact algorithms. We also identify several problem areas and issues for future research.

Integrated Production and Outbound Distribution Scheduling: Review and Extensions

https://pure.tue.nl/ws/files/2129202/403141.pdf

Preemptive scheduling in a two-stage multiprocessor flow shop is np-hard

This paper adresses certain types of scheduling problems that arise when a parallel computation is to be executed on a multiprocessor. We define a model that allows for communication delays between precedence-related tasks, and propose a classification of various submodels. We also review complexity results and optimization and approximation algorithms that have been presented in the literature.

/pdf/multiprocessor-scheduling-with-communication-delays-5fiv2cbbqq.pdf

Multiprocessor scheduling with communication delays

https://pure.tue.nl/ws/files/1860008/403142.pdf

Three, four, five, six, or the complexity of scheduling with communication delays

A set of unit-time tasks has to be processed on identical parallel processors subject to precedence constraints and unit-time communication delays; does there exist a schedule of length at most d? The problem has two variants, depending on whether the number of processors is restrictively small or not. For the first variant the question can be answered in polynomial time for d = 3 and is NP-complete for d = 4. The second variant is solvable in polynomial time for d = 5 and NP-complete for d = 6. As a consequence, neither of the corresponding optimization problems has a polynomial approximation scheme, unless P = NP.

textWe investigate the computational complexity of scheduling multiprocessor tasks with prespecified processor allocations. We consider two criteria: minimizing schedule length and minimizing the sum of the task completion times. In addition, we investigate the complexity of problems when precedence constraints or release dates are involved.

Complexity of scheduling multiprocessor tasks with prespecified processor allocations

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Papers

Preemptive scheduling in a two-stage multiprocessor flow shop is np-hard

Multiprocessor scheduling with communication delays

Three, four, five, six, or the complexity of scheduling with communication delays

Three, four, five, six, or the complexity of scheduling with communication delays

Complexity of scheduling multiprocessor tasks with prespecified processor allocations