Optimal Off-line Algorithm Research Articles

Advance Service Reservations with Heterogeneous Customers

We study a fundamental model of resource allocation in which a finite number of resources must be assigned in an online manner to a heterogeneous stream of customers. The customers arrive randomly over time according to known stochastic processes. Each customer requires a specific amount of capacity and has a specific preference for each of the resources with some resources being feasible for the customer and some not. The system must find a feasible assignment of each customer to a resource or must reject the customer. The aim is to maximize the total expected capacity utilization of the resources over the horizon. This model has application in services, freight transportation, and online advertising. We present online algorithms with bounded competitive ratios relative to an optimal off-line algorithm that knows all stochastic information. Our algorithms perform extremely well compared with common heuristics as demonstrated on a real data set from a large hospital system in New York City. This paper was accepted by Yinyu Ye, optimization.

An efficient method to evaluate intersections on big data sets

Set intersections are important in computer science. Especially, intersection of inverted lists is a fundamental operation in information retrieval for text databases and Web search engines. In this paper, we discuss an efficient and effective way to implement this operation in the context of very big data sets. The main idea behind it is to do a binary search over sorted interval sequences, each of which corresponds to an inverted list and is constructed by establishing a trie over the sequences of set identifiers as well as a kind of tree encoding, by which each node in the trie is assigned an interval. In many cases, an interval sequence is much shorter than its corresponding inverted list. In particular, the lowest common ancestors of intervals in a trie can be utilized to control a binary search to skip over useless interval containment checks, which enables us to reach an optimal off-line algorithm to do the task, and is theoretically better than any traditional on-line methods (at cost of more space). Experiments have been conducted, showing that the trade-off of space for time is worthwhile.

Throughput Optimal Policies for Energy Harvesting Wireless Transmitters with Non-Ideal Circuit Power

Characterizing the fundamental tradeoffs for maximizing energy efficiency (EE) versus spectrum efficiency (SE) is a key problem in wireless communication. In this paper, we address this problem for a point-to-point additive white Gaussian noise (AWGN) channel with the transmitter powered solely via energy harvesting from the environment. In addition, we assume a practical on-off transmitter model with non-ideal circuit power, i.e., when the transmitter is on, its consumed power is the sum of the transmit power and a constant circuit power. Under this setup, we study the optimal transmit power allocation to maximize the average throughput over a finite horizon, subject to the time-varying energy constraint and the non-ideal circuit power consumption. First, we consider the off-line optimization under the assumption that the energy arrival time and amount are a priori known at the transmitter. Although this problem is non-convex due to the non-ideal circuit power, we show an efficient optimal solution that in general corresponds to a two-phase transmission: the first phase with an EE-maximizing on-off power allocation, and the second phase with a SE-maximizing power allocation that is non-decreasing over time, thus revealing an interesting result that both the EE and SE optimizations are unified in an energy harvesting communication system. We then extend the optimal off-line algorithm to the case with multiple parallel AWGN channels, based on the principle of nested optimization. Finally, inspired by the off-line optimal solution, we propose a new online algorithm under the practical setup with only the past and present energy state information (ESI) known at the transmitter.

Discrete optimal control for robot manipulators

Purpose – Applying discrete linear optimal control to robot manipulators faces two challenging problems, namely nonlinearity and uncertainty. This paper aims to overcome nonlinearity and uncertainty to design the discrete optimal control for electrically driven robot manipulators. Design/methodology/approach – Two novel discrete optimal control approaches are presented. In the first approach, a control-oriented model is applied for the discrete linear quadratic control while modeling error is estimated and compensated by a robust time-delay controller. Instead of the torque control strategy, the voltage control strategy is used for obtaining an optimal control that is free from the manipulator dynamics. In the second approach, a discrete optimal controller is designed by using a particle swarm optimization algorithm. Findings – The first controller can overcome uncertainties, guarantee stability and provide a good tracking performance by using an online optimal algorithm whereas the second controller is an off-line optimal algorithm. The first control approach is verified by stability analysis. A comparison through simulations on a three-link electrically driven robot manipulator shows superiority of the first approach over the second approach. Another comparison shows that the first approach is superior to a bounded torque control approach in the presence of uncertainties. Originality/value – The originality of this paper is to present two novel optimal control approaches for tracking control of electrically driven robot manipulators with considering the actuator dynamics. The novelty is that the proposed control approaches are free from the robot's model by using the voltage control strategy. The first approach is a novel discrete linear quadratic control design supported by a time-delay uncertainty compensator. The second approach is an off-line optimal design by using the particle swarm optimization.

A new approach to solve the k-server problem based on network flows and flow cost reduction

This paper is concerned with two algorithms for solving the k-server problem: the optimal off-line algorithm (OPT) and the on-line work function algorithm (WFA). Both algorithms are usually implemented by network flow techniques including the flow augmentation method. In the paper a new implementation approach is proposed, which is again based on network flows, but uses simpler networks and the cost reduction method. The paper describes in detail the corresponding new implementations of OPT and WFA, respectively. All necessary correctness proofs are given. Also, experiments are presented, which confirm that the new approach assures faster execution of both algorithms.

WORST-CASE PERFORMANCE EVALUATION ON MULTIPROCESSOR TASK SCHEDULING WITH RESOURCE AUGMENTATION

We study the worst-case performance of approximation algorithms for the problem of multiprocessor task scheduling on m identical processors with resource augmentation, whose objective is to minimize the makespan. In this case, the approximation algorithms are given k (k ≥ 0) extra processors than the optimal off-line algorithm. For on-line algorithms, the Greedy algorithm and shelf algorithms are studied. For off-line algorithm, we consider the LPT (longest processing time) algorithm. Particularly, we prove that the schedule produced by the LPT algorithm is no longer than the optimal off-line algorithm if and only if k ≥ m - 2.

Buffer Management Algorithms in Unbounded Buffers

In a network router, packet loss may occur when it overflows due to sudden burst traffic. This paper studies how much large buffers are required to eliminate the packet losses. There are buffers on which packets arrive and one output port to which a packet is transmitted at a time. The buffer management algorithm should determine one of the buffers whose packet is transmitted to the output port at each time. The front packet belonging to the buffer determined by the algorithm is transmitted. The goal is to minimize the sum of the lengths of buffers to transmit all the packets. We provide an optimal off-line algorithm and also we show the lower bounds of on-line algorithms. The online algorithm has no prior information of the packets having arrived in the future. Its performance is compared to that of the optimal off-line algorithm.

Proxy caching for peer-to-peer live streaming

Peer-to-Peer (P2P) live streaming has become increasingly popular over the Internet. To alleviate the inter-ISP traffic load and to minimize the access latency, proxy caching has been widely suggested for P2P applications. In this paper, we carry out an extensive measurement study on the properties of P2P live streaming data requests. Our measurement demonstrates that the P2P living streaming traffic exhibits strong localities that could be explored by caching. This is particularly noticeable for the temporal locality, which is often much weaker in the conventional P2P file sharing applications. Our results further suggest that the request time of the same data piece from different peers exhibits a generalized extreme value distribution. We then propose a novel sliding window (SLW)-based caching algorithm, which predicts and caches popular data pieces according to the measured distribution. Our experimental results suggest that the P2P live streaming can greatly benefit from the proxy caching. And, with much lower overhead, our SLW algorithm works closer to an off-line optimal algorithm that holds the complete knowledge of future requests.

Dynamic TCP acknowledgment with sliding window

The dynamic TCP acknowledgement problem which focuses the acknowledgment mechanism in TCP protocol has been intensively studied in the area of competitive analysis. However, its framework does not consider the sliding window in the TCP protocol that restricts the maximum number of packets that the sender can inject into the network without an acknowledgement. This paper proposes a new problem in which the sliding window is realistically integrated. We study how the ability of on-line algorithms changes, depending on whether the receiver is taught the window size. The greater part of this paper assumes that the window size is a constant integer W . We first show that, if W is given, the optimal on-line algorithm for the previous framework can be extended to our new framework and achieves the optimal competitive ratio of 2. Next we prove that, if W is not given, the lower bound of the competitive ratio for an algorithm class which contains the optimal algorithm for the previous framework depends on the peak packet rate T from the sender and W , and is not better than ( T W + ⌊ T W ⌋ − 1 ) -competitive. Then, we prove that there exists an on-line algorithm that is ( ⌈ T W ⌉ + 2 ) -competitive, when W is unknown. An optimal off-line algorithm is also presented in this paper. Significantly, our problem models the situation in which an on-line algorithm involuntarily transforms the input and processes the modified input without noticing the transformation.

Traffic Modeling and Proportional Partial Caching for Peer-to-Peer Systems

Peer-to-peer (P2P) file sharing systems generate a major portion of the Internet traffic, and this portion is expected to increase in the future. We explore the potential of deploying proxy caches in different autonomous systems (ASes) with the goal of reducing the cost incurred by Internet service providers and alleviating the load on the Internet backbone. We conduct an eight-month measurement study to analyze the P2P traffic characteristics that are relevant to caching, such as object popularity, popularity dynamics, and object size. Our study shows that the popularity of P2P objects can be modeled by a Mandelbrot-Zipf distribution, and that several workloads exist in P2P traffic. Guided by our findings, we develop a novel caching algorithm for P2P traffic that is based on object segmentation, and proportional partial admission and eviction of objects. Our trace-based simulations show that with a relatively small cache size, a byte hit rate of up to 35% can be achieved by our algorithm, which is close to the byte hit rate achieved by an off-line optimal algorithm with complete knowledge of future requests. Our results also show that our algorithm achieves a byte hit rate that is at least 40% more, and at most triple, the byte hit rate of the common Web caching algorithms. Furthermore, our algorithm is robust in face of aborted downloads, which is a common case in P2P systems.

On Dynamic Bin Packing: An Improved Lower Bound and Resource Augmentation Analysis

We study the dynamic bin packing problem introduced by Coffman, Garey and Johnson. This problem is a generalization of the bin packing problem in which items may arrive and depart from the packing dynamically. The main result in this paper is a lower bound of 2.5 on the achievable competitive ratio, improving the best known 2.428 lower bound, and revealing that packing items of restricted form like unit fractions (i.e., of size 1/k for some integer k), for which a 2.4985-competitive algorithm is known, is indeed easier. We also investigate the resource augmentation version of the problem where the on-line algorithm can use bins of size b (>1) times that of the optimal off-line algorithm. An interesting result is that we prove b=2 is both necessary and sufficient for the on-line algorithm to match the performance of the optimal off-line algorithm, i.e., achieve 1-competitiveness. Further analysis gives a trade-off between the bin size multiplier 1<b≤2 and the achievable competitive ratio.

Reward-based voltage scheduling for dynamic-priority hard real-time systems

Reward-based scheduling has been investigated for flexible applications in which an approximate but timely result is acceptable. Meanwhile, significant research efforts have been made on voltage scheduling which exploits the tradeoff between the processor speed and the energy consumption. In this paper, we address the combined scheduling problem of maximizing the total reward of hard real-time systems with a given energy budget. We present an optimal off-line algorithm and an efficient on-line algorithm for jobs with their own release-times/deadlines under Earliest-Deadline-First (EDF) scheduling. Experimental results show that the solution computed by the on-line algorithm is no more than 14% worse than the theoretical optimal solution obtained by the optimal off-line algorithm.

Approximation algorithms for scheduling real-time jobs with multiple feasible intervals

Time-critical jobs in many real-time applications have multiple feasible intervals. Such a job is constrained to execute from start to completion in one of its feasible intervals. A job fails if the job remains incomplete at the end of the last feasible interval. Earlier works developed an optimal off-line algorithm to schedule all the jobs in a given job set and on-line heuristics to schedule the jobs in a best effort manner. This paper is concerned with how to find a schedule in which the number of jobs completed in one of their feasible intervals is maximized. We show that the maximization problem is \({\cal N}{\cal P}\)-hard for both non-preemptible and preemptible jobs. This paper develops two approximation algorithms for non-preemptible and preemptible jobs. When jobs are non-preemptible, Algorithm Least Earliest Completion Time First (LECF) is shown to have a 2-approximation factor; when jobs are preemptible, Algorithm Least Execution Time First (LEF) is proved being a 3-approximation algorithm. We show that our analysis for the two algorithms are tight. We also evaluate our algorithms by extensive simulations. Simulation results show that Algorithms LECF and LEF not only guarantee the approximation factors but also outperform other multiple feasible interval scheduling algorithms in average.

Optimizing the quality of scalable video streams on P2P networks

The volume of multimedia data, including video, served through Peer-to-Peer (P2P) networks is growing rapidly. Unfortunately, high bandwidth transfer rates are rarely available to P2P clients on a consistent basis. In addition, the rates are more variable and less predictable than in traditional client-server environments, making it difficult to use P2P networks to stream video for on-line viewing rather than for delayed playback.In this paper, we develop and evaluate on-line algorithms that coordinate the pre-fetching of scalably-coded variable bit-rate video. These algorithms are ideal for P2P environments in that they require no knowledge of the future variability or availability of bandwidth, yet produce a playback whose average rate and variability are comparable to the best off-line pre-fetching algorithms that have total future knowledge. To show this, we develop an off-line algorithm that provably optimizes quality and variability metrics. Using simulations based on actual P2P traces, we compare our on-line algorithms to the optimal off-line algorithm and find that our novel on-line algorithms exhibit near-optimal performance and significantly outperform more traditional pre-fetching methods.

Optimal on-line flow time with resource augmentation

We study the problem of scheduling n jobs that arrive over time. We consider a non-preemptive setting on a single machine. The goal is to minimize the total flow time. We use extra resource competitive analysis: an optimal off-line algorithm which schedules jobs on a single machine is compared to a more powerful on-line algorithm that has ℓ machines. We design an algorithm of competitive ratio 1 + 2 min ( Δ 1 / ℓ , n 1 / ℓ ) , where Δ is the maximum ratio between two job sizes, and provide a lower bound which shows that the algorithm is optimal up to a constant factor for any constant ℓ . The algorithm works for a hard version of the problem where the sizes of the smallest and the largest jobs are not known in advance, only Δ and n are known. This gives a trade-off between the resource augmentation and the competitive ratio. We also consider scheduling on parallel identical machines. In this case the optimal off-line algorithm has m machines and the on-line algorithm has ℓ m machines. We give a lower bound for this case. Next, we give lower bounds for algorithms using resource augmentation on the speed. Finally, we consider scheduling with hard deadlines, and scheduling so as to minimize the total completion time.

Off-line and on-line guaranteed start-up delay for Media-on-Demand with stream merging

We address the problem of designing efficient algorithms for media-on-demand in systems that use stream merging. In the stream merging model the receiving bandwidth of clients is larger than the playback bandwidth, and clients can buffer parts of the transmission to be played back later. Our goal is to minimize the required server bandwidth for a given guaranteed start-up delay and uninterrupted playback. We construct an efficient O ( n ) optimal off-line algorithm for a time horizon that is composed of n time slots, where the length of one slot is the guaranteed start-up delay. Our algorithm works for either clients with receiving bandwidth twice as much as the playback bandwidth or for receiving bandwidth equal to the server bandwidth, independent of the clients buffer size. We describe an on-line delay guaranteed algorithm that operates without knowledge of the time horizon size, and show that it performs asymptotically close to the optimal off-line algorithm. The on-line algorithm is simpler to implement than previously proposed on-line stream merging algorithms, and empirically performs well when the intensity of client arrivals is high.

Seat reservation allowing seat changes

We consider a variant of the Seat Reservation Problem [J. Boyar, K.S. Larsen, Algorithmica 25 (1999) 403–417] in which seat changes are allowed. We analyze the model using the competitive ratio, the competitive ratio on accommodating sequences [J. Boyar, K.S. Larsen, Algorithmica 25 (1999) 403–417], and the accommodating function [J. Boyar et al., Acta Informatica 40 (2003) 3–35; J. Boyar et al., SIAM J. Comput. 31 (1) (2001) 233–258]. A very promising family of algorithms considered in this paper is Min-Change, which will ask passengers to change seats, only if they would otherwise have been rejected. Min-Change belongs to a large class of conservative algorithms, which all have very high performance guarantees. For instance, if the optimal off-line algorithm can seat all of the passengers, 2/3 of the passengers can be seated on-line using any conservative algorithm allowing only one seat change and 3/4 will be seated if two seat changes are allowed. This should be compared to the asymptotic hardness result of 1/2 for the best algorithm when no seat changes are allowed [E. Bach et al., J. Sched. 6 (2003) 131–147]. Another interesting algorithm, Modified-Kierstead–Trotter, is proposed and shown to seat all passengers if the optimal off-line algorithm could have accommodated them with only half as many seats. On this type of sequence, Modified-Kierstead–Trotter is strictly better than Min-Change-First-Fit which is strictly better than the Checkerboard algorithm.

Analysis of simple randomized buffer management for parallel I/O

Buffer management for a D-disk parallel I/O system is considered in the context of randomized placement of data on the disks. A simple prefetching and caching algorithm PHASE-LRU using bounded lookahead is described and analyzed. It is shown that PHASE-LRU performs an expected number of I/Os that is within a factor Θ(log D/loglog D) of the number performed by an optimal off-line algorithm. In contrast, any deterministic buffer management algorithm with the same amount of lookahead must do at least Ω( D ) times the number of I/Os of the optimal.

Efficient Algorithms for Optimal Stream Merging for Media-on-Demand

We address the problem of designing optimal off-line algorithms that minimize the required bandwidth for media-on-demand systems that use stream merging. We concentrate on the case where clients can receive two media streams simultaneously and can buffer up to half of a full stream. We construct an O(nm) optimal algorithm for n arbitrary time arrivals of clients, where m is the average number of arrivals in an interval of a stream length. We then show how to adopt our algorithm to be optimal even if clients have a limited size buffer. The complexity remains the same. We also prove that using stream merging may reduce the required bandwidth by a factor of order $\rho L/\log(\rho L)$ compared to the simple batching solution where L is the length of a stream and $\rho\le 1$ is the density in time of all the n arrivals. On the other hand, we show that the bandwidth required when clients can receive an unbounded number of streams simultaneously is always at least 1/2 the bandwidth required when clients are limited to receiving at most two streams.

Flood search under the California Split rule

We consider flood search on a line and show that no algorithm can achieve an average-case competitive ratio of less than 4 when compared to the optimal off-line algorithm. We also demonstrate that the optimal scanning sequences are described by simple recursive relationships that yield surprisingly complex behavior related to Hamiltonian chaos.