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The analysis of a posteriori error estimates used in reduced basis methods leads to a model reduction scheme for linear time-invariant systems involving the iterative approximation of the associated error systems. The scheme can be used to improve reduced-order models (ROMs) with initial poor approximation quality at a computational cost proportional to that for computing the original ROM. We also show that the iterative approximation scheme is applicable to parametric systems and demonstrate its performance using illustrative examples. [ABSTRACT FROM AUTHOR]

One of the most important issues in the design of distributed systems is process scheduling, which maps applications to resources in an attempt to reduce the application execution time or maximise resource utilisation. The complexity involved in finding good scheduling solutions has motivated the design of several heuristics and approximation algorithms. Although heuristics aim at finding good solutions within acceptable time constraints, they do not guarantee solution quality. On the other hand, approximation-based algorithms provide optimal solution bounds, but they are usually designed to address simple scenarios. In an attempt to combine the best of both algorithmic approaches, this paper proposes the min-heap-based scheduling algorithm (MHSA), which finds solutions for homogeneous and heterogeneous distributed environments within acceptable time constraints and optimal solution bounds. MHSA considers applications that can be bag-of-tasks or which communicate among each other. Such solutions minimise the application execution time and maximise resource utilisation; therefore, MHSA is a system-oriented scheduling algorithm. Results confirm that MHSA provides better solutions than schedulers such as Random, Round-Robin, Workload-Queue and List-Scheduling. In addition, MHSA provides an-approximation ratio for reaching optimal solution bounds. [ABSTRACT FROM AUTHOR]

This article considers the problems of scheduling operations in single-gripper and dual-gripper bufferless robotic cells in which the arrangement of machines is circular. The cells are designed to produce identical parts under the free-pickup criterion with additive intermachine travel time. The objective is to find a cyclic sequence of robot moves that minimizes the long-run average time required to produce a part or, equivalently, that maximizes the throughput. Obtaining an efficient algorithm for an approximation to an optimalk-unit cyclic solution (over allk≥ 1) is the focus of this article. The proposed algorithms introduce a new class of schedules, which are refered to as epi-cyclic cycles. A polynomial algorithm with a 5/3-approximation to an optimalk-unit cycle over all cells is developed. The performed structural analysis for dual-gripper cells leads to a polynomial-time algorithm that provides at worst a 3/2-approximation for the practically relevant case in which the dual-gripper switch time is less than twice the intermachine robot movement time. A computational study demonstrates that the algorithm performs much better on average than this worst-case bound suggests. The performed theoretical studies are a stepping stone for researching the complexity status of the corresponding domain. They also provide theoretical as well as practical insights that are useful in maximizing productivity of any cell configuration with either type of robot. [ABSTRACT FROM PUBLISHER]

This paper presents a new polynomial-time algorithm, approximate star bicoloring (ASBC), for star bicoloring and acyclic bicoloring. These NP-complete combinatorial problems arise from problems associated with computing large sparse Jacobian matrices. The main results of this paper lie in approximation analysis related to these problems. In particular, it is shown that (i) both star and acyclic bicoloring can be approximated in polynomial time to the ratio O(n 2/3) and (ii) both star and acyclic bicoloring cannot be approximated to the ratio O(n 1/3−ε) in polynomial time under reasonable complexity theoretic hypotheses. The ASBC algorithm is also analysed experimentally on a collection of realistic test cases from the Harwell–Boeing sparse matrix collection. The experimental results indicate that ASBC performs quite well in practice; the performance of the new algorithm always fell within the range of 1.53 and 6 times optimal on the given test sets. [ABSTRACT FROM AUTHOR]

To improve reachability of a snake-like robot depending on the problem, the links of the robot need to be resizable. In such a case folding links of the robot help to better plan obstacle avoidance. Optimum folding of the robot is the aim of our paper. We introduce a practical idea to construct reconfigurable and resizable snake robots which can be folded and an approximation algorithm to find near-optimum folding for the robot. Since an open chain is an abstract model of a snake-like robot, folding algorithms for the proposed robot are given in terms of an open chain. Ruler folding is a well-known NP-Complete problem. It considers folding of an n-link open chain linkage to the minimum length. The best previously known approximation algorithm for this problem has been developed by Hopcroft et al. They achieved the upper bound of 2m1 for the length of the folded chain in all cases, where m1 is the length of the longest link of the given chain. Already there are no any algorithms for open chain folding which guarante that the folded length of the open chain is less than 2m1. In this paper, we introduce an approximation algorithm which runs in O (n log n) using O (n) space. We introduce a function for the upper bound of the folded chain which depends to the lengths of all links in the given chain. Our experimental results show that for more than 95% of the problem instances we can achieve the same results in O (n) time. Using our folding algorithm, we can design the length of each link in an open chain to get x · m1 folded length where 1 < x < 2 is given and m1 is the length of the longest link of the chain. We introduce how to design a snake-like robot for which it can be folded in the given interval. [ABSTRACT FROM AUTHOR]

In this note a tight worst-case ratio bound is derived for a heuristic for the three-stage flexible flowshop makespan minimization problem. It is shown that the derived bound is the best available for the three-stage problem. Furthermore, the derived bound can be used to improve the best available worst-case ratio bound for the flexible flowshop makespan minimization problem with an arbitrary odd number of stages. [ABSTRACT FROM AUTHOR]

This paper considers the problem of scheduling operations in bufferless robotic cells that produce identical parts. Finding a cyclic solution that minimizes the long-run average time to produce a part has long been a fundamental open problem. Most research has been focused on finding an optimal 1-unit cyclic solution. However, it is known that an optimal multi-unit cyclic solution can be better than an optimal 1-unit cyclic solution for cells with four or more machines. For additive travel-time cells, we present a linear-time algorithm that produces a cyclic solution whose per unit cycle time is within a factor of 10/7 of the optimum. This result improves the current best 3/2-approximation guarantee. [ABSTRACT FROM AUTHOR]

Given a translating and rotating rod robot in a plane in the presence of polygonal obstacles with the initial and final placements of the rod known, the d 1 -optimal motion planning problem is defined as finding a collision-free motion of the rod such that the orbit length of a fixed but arbitrary point F on the rod is minimized. In this paper we study a special case of this problem in which the rod can translate freely, but can only rotate by some pre-specified given angles around F . We first characterize the d 1 -optimal motion of the robot under the given conditions and then present a (1 + ε)–approximation algorithm for finding the optimal path. The running time of the algorithm is bounded by a polynomial in terms of some parameters related to the problem input. [ABSTRACT FROM AUTHOR]