Abstract In the classic minimum makespan scheduling problem, we are given an input sequence of n jobs with sizes. A scheduling algorithm has to assign the jobs to m parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, we consider online scheduling algorithms without preemption. However, we allow the online algorithm to change the assignment of up to k jobs at the end for some limited number k. For m identical machines, Albers and Hellwig (Algorithmica 79(2):598–623, 2017) give tight bounds on the competitive ratio in this model. The precise ratio depends on, and increases with, m. It lies between 4/3 and $$\approx 1.4659$$ ≈ 1.4659 . They show that $$k = O(m)$$ k = O ( m ) is sufficient to achieve this bound and no $$k = o(n)$$ k = o ( n ) can result in a better bound. We study m uniform machines, i.e., machines with different speeds, and show that this setting is strictly harder. For sufficiently large m, there is a $$\delta = \varTheta (1)$$ δ = Θ ( 1 ) such that, for m machines with only two different machine speeds, no online algorithm can achieve a competitive ratio of less than $$1.4659 + \delta $$ 1.4659 + δ with $$k = o(n)$$ k = o ( n ) . We present a new algorithm for the uniform machine setting. Depending on the speeds of the machines, our scheduling algorithm achieves a competitive ratio that lies between 4/3 and $$\approx 1.7992$$ ≈ 1.7992 with $$k = O(m)$$ k = O ( m ) . We also show that $$k = \varOmega (m)$$ k = Ω ( m ) is necessary to achieve a competitive ratio below 2. Our algorithm is based on maintaining a specific imbalance with respect to the completion times of the machines, complemented by a bicriteria approximation algorithm that minimizes the makespan and maximizes the average completion time for certain sets of machines.

In the classic minimum makespan scheduling problem, we are given an input sequence of n jobs with sizes. A scheduling algorithm has to assign the jobs to m parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, we consider online scheduling algorithms without preemption. However, we allow the online algorithm to reassign up to k jobs to different machines in the final assignment. For m identical machines, Albers and Hellwig (Algorithmica, 2017) give tight bounds on the competitive ratio in this model. The precise ratio depends on, and increases with, m. It lies between 4/3 and ~~ 1.4659. They show that k = O(m) is sufficient to achieve this bound and no k = o(n) can result in a better bound. We study m uniform machines, i.e., machines with different speeds, and show that this setting is strictly harder. For sufficiently large m, there is a delta = Theta(1) such that, for m machines with only two different machine speeds, no online algorithm can achieve a competitive ratio of less than 1.4659 + delta with k = o(n). We present a new algorithm for the uniform machine setting. Depending on the speeds of the machines, our scheduling algorithm achieves a competitive ratio that lies between 4/3 and ~~ 1.7992 with k = O(m). We also show that k = Omega(m) is necessary to achieve a competitive ratio below 2. Our algorithm is based on a subtle imbalance with respect to the completion times of the machines, complemented by a bicriteria approximation algorithm that minimizes the makespan and maximizes the average completion time for certain sets of machines.

We consider the problem of online packet scheduling in Combined Input and Output Queued (CIOQ) and buffered crossbar switches. In the widely used CIOQ switches, packet buffers (queues) are placed at both input and output ports. An N x N CIOQ switch has N input ports and N output ports, where each input port is equipped with N queues, each of which corresponds to an output port, and each output port is equipped with only one queue. In each time step, arbitrarily many packets may arrive at each input port, and only one packet can be transmitted from each output port. Packets are transferred from the queues of input ports to the queues of output ports through the internal fabric. Buffered crossbar switches follow a similar design, but are equipped with additional buffers in their internal fabric. In either model, our goal is to maximize the number or, in case the packets have weights, the total weight of transmitted packets.

In the classic minimum makespan scheduling problem, we are given an input sequence of jobs with processing times. A scheduling algorithm has to assign the jobs to $m$ parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, we consider online scheduling algorithms without preemption. However, we do not require that each arriving job has to be assigned immediately to one of the machines. A reordering buffer with limited storage capacity can be used to reorder the input sequence in a restricted fashion so as to schedule the jobs with a smaller makespan. This is a natural extension of lookahead. We present an extensive study of the power and limits of online reordering for minimum makespan scheduling. As a main result, we give, for $m$ identical machines, tight and, in comparison to the problem without reordering, much improved bounds on the competitive ratio for minimum makespan scheduling with reordering buffers. Depending on $m$, the achieved competitive ratio lies between 4/3 and 1.4659. This optimal ratio is achieved with a buffer of size $\Theta(m)$. We show that larger buffer sizes do not result in an additional advantage and that a buffer of size $\Omega(m)$ is necessary to achieve this competitive ratio. Further, we present several algorithms for different buffer sizes. For $m$ uniformly related machines, we give a scheduling algorithm that achieves a competitive ratio of 2 with a reordering buffer of size $m$. Considering that the best known competitive ratio for uniformly related machines without reordering is 5.828, this result further emphasizes the power of online reordering.

The following buffer management problem arises in network switches providing different levels of services: At the beginning of each time step, one packet can be sent, and afterward an arbitrary number of new packets arrive. Packets that are not sent can be stored in a buffer. Each packet has a deadline, and a packet is automatically deleted from the buffer if it is still stored in the buffer by the end of its deadline. Additionally, each packet has a value which reflects its importance. A buffer management strategy determines the packet to be sent in each time step. The goal of a buffer management strategy is to maximize the sum of the values of sent packets. We introduce the concept of suppressed packets and present a deterministic strategy that is based on this concept. We show that this strategy achieves a competitive ratio of $2 \sqrt{2} - 1 \approx 1.828$, which is the best known competitive ratio in the deterministic case. In addition, we present a memoryless version of this strategy that achieves a competitive ratio of $\approx 1.893$. This is the first memoryless strategy that achieves a competitive ratio less than 2. Altogether, this demonstrates the potential of the concept of suppressed packets.

In the classic minimum makespan scheduling problem, we are given an input sequence of jobs with processing times. A scheduling algorithm has to assign the jobs to m parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, we consider online scheduling algorithms without preemption. However, we do not require that each arriving job has to be assigned immediately to one of the machines. A reordering buffer with limited storage capacity can be used to reorder the input sequence in a restricted fashion so as to schedule the jobs with a smaller makespan. This is a natural extension of lookahead.We present an extensive study of the power and limits of online reordering for minimum makespan scheduling. As main result, we give, for m identical machines, tight and, in comparison to the problem without reordering, much improved bounds on the competitive ratio for minimum makespan scheduling with reordering buffers. Depending on m, the achieved competitive ratio lies between 4/3 and 1.4659. This optimal ratio is achieved with a buffer of size Theta(m). We show that larger buffer sizes do not result in an additional advantage and that a buffer of size Omega(m) is necessary to achieve this competitive ratio. Further, we present several algorithms for different buffer sizes. Among others, we introduce, for every buffer size k

In the reordering buffer problem, we are given an input sequence of requests for service each of which corresponds to a point in a metric space. The cost of serving the requests heavily depends on the processing order. Serving a request induces cost corresponding to the distance between itself and the previously served request, measured in the underlying metric space. A reordering buffer with storage capacity k can be used to reorder the input sequence in a restricted fashion so as to construct an output sequence with lower service cost. This simple and universal framework is useful for many applications in computer science and economics, e.g., disk scheduling, rendering in computer graphics, or painting shops in car plants.

We consider distributed caching strategies for networks in a model that takes in addition to remote accesses also local accesses into account. The goal is to minimize the congestion while obeying memory capacity constraints in the network. The on-line strategies are evaluated in a competitive analysis in which their costs are compared with the cost of an optimal off-line strategy. Previous results either depend on the network size or assume that the on-line strategies have increased memory capacity constraints in comparison to an optimal off-line strategy.(MATH) Our main result is a strategy for complete networks. For each node v, we are given memory capacity m(v) and load d(v) for a remote access. The load for a local access is one. For each application concerning a set X of shared data objects, with |X| ≤ Σv m(v) / d(v), the strategy achieves a competitive ratio of

This paper deals with static data management in computer systems connected by networks. A basic functionality in these systems is the interactive use of shared data objects that can be accessed from each computer in the system. Examples for these objects are files in distributed file systems, cache lines in virtual shared memory systems, or pages in the WWW. In the static scenario we are given read and write request frequencies for each computer-object pair. The goal is to calculate a placement of the objects to the memory modules, possibly with redundancy, such that a given cost function is minimized.

A hierarchical bus network T = (V, E) uses hierarchically, tree-like connected buses as a communication network. New communication technologies like SCI (Scalable Coherent Interface) (see, e.g., [6, 7]) make such networks very attractive, because they allow their easy construction and guarantee reasonable communication performance. Such networks can be modeled as tree networks: leaves correspond to processors, inner nodes to buses, edges to switches, and bandwidths of inner nodes and edges are related to bandwidths of buses and switches, respectively.

This paper deals with data management for parallel and distributed systems. We present the DIVA (Distributed Variables ) library that provides direct access to shared data objects from each node in a network. The current implementations are based on mesh-connected massively parallel computers. Our algorithms dynamically create and discard copies of the data objects in order to reduce the communication overhead. We use a non-standard approach based on a randomized but locality preserving embedding of ``access trees'' into the network.

This paper deals with data management in computer systems in which the computing nodes are connected by a relatively sparse network. We consider the problem of placing and accessing a set of shared objects that are read and written from the nodes in the network. These objects are, e.g., global variables in a parallel program, pages or cache lines in a virtual shared memory system, shared files in a distributed file system, or pages in the World Wide Web. A data management strategy consists of a placement strategy that maps the objects (possibly dynamically and with redundancy) to the nodes, and an access strategy that describes how reads and writes are handled by the system (including the routing). We investigate static and dynamic data management strategies.