Lower bounds on the performance of online algorithms for relaxed packing problems

We prove new lower bounds for suitable competitive ratio measures of two relaxed online packing problems: online removable multiple knapsack, and a recently introduced online minimum peak appointment scheduling problem. The high level objective in both problems is to pack arriving items of sizes at most 1 into bins of capacity 1 as efficiently as possible, but the exact formalizations differ. In the appointment scheduling problem, every item has to be assigned to a position, which can be seen as a time interval during a workday of length 1. That is, items are not assigned to bins, but only once all the items are processed, the optimal number of bins subject to chosen positions is determined, and this is the cost of the online algorithm. On the other hand, in the removable knapsack problem there is a fixed number of bins, and the goal of packing items, which consists in choosing a particular bin for every packed item (and nothing else), is to pack as valuable a subset as possible. In this last problem it is possible to reject items, that is, deliberately not pack them, as well as to remove packed items at any later point in time, which adds flexibility to the problem.KeywordsBin packingOnline algorithmsCompetitive ratio

In this paper we presented a novel on-line adaptive recursive algorithm which is capable of resolving multiple coherent spatial sources, as is often the case in radar situation. Most of the adaptive beamforming algorithms fail to operate in such situation or their performance will be degraded. Our algorithm is based upon the travelling antenna concept introduced by Gabriel [1]. We test the performance of this algorithm using computer simulation. An eight-element array involving coherent sources of equal and unequal strength are used for the test. We compared the performance of this algorithm with the performance of the SMI algorithm. We find that this algorithm can successfully seperate two coherent sources.

The explosive growth of Web-related services over the Internet is bringing millions of new users online, thus creating a growing demand for bandwidth. Wavelength Division Multiplexed (WDM) networks, employing wavelength routing has emerged as the dominant technology to satisfy this growing demand for bandwidth. As the amount of traffic carried is larger, any single failure can be catastrophic. Survivability becomes indispensable in such networks. Therefore, it is imperative to design networks that can quickly and efficiently recover from failures.;In this dissertation, we explore the design and operation of survivable optical networks. We study several survivability paradigms for surviving single link failures. A restoration model is developed based on a combination of these paradigms. We propose an optimal design and upgrade scheme for WDM backbone networks. We formulate an integer programming-based design problem to minimize the total facility cost. This framework provides a cost effective way of upgrading the network by identifying how much resources to budget at each stage of network evolution. This results in significant cost reductions for the network service provider.;As part of network operation, we capture multiple operational phases in survivable network operation as a single integer programming formulation. This common framework incorporates service disruption and includes a service differentiation model based on lightpath protection. However, the complexity of the optimization problem makes the formulation applicable only for network provisioning and o2ine reconfiguration. The direct use of such methods for online reconfiguration remains limited to small networks with few tens of wavelengths. We develop a heuristic algorithm based on LP relaxation technique for fast, near optimal, online reconfiguration. Since the ILP variables are relaxed, we provide a way to derive a feasible solution from the relaxed problem. Most of the current approaches assume centralized information. They do not scale well as they rely on per-flow information. This motivates the need for developing dynamic algorithms based on partial information. The partial information we use can be easily obtained from traffic engineering extensions to routing protocols. Finally, the performance of partial information routing algorithms is compared through simulation studies.

Recently, a number of WiFi access points (APs) have been densely deployed to provide widely available, high-performance Internet services. As such, an energy efficiency issue becomes crucial toward the design of green wireless local area networks (WLANs). In this paper, we propose a resource and re-association scheduling algorithm (referred to RAS) based on Benders' decomposition to reduce the energy consumption. In particular, we endeavor to aggregate WLAN users on the small number of APs and turn off many APs without compromising users' quality of experience (QoE) and system coverage. We conduct the analysis by using real trace data and formulate the energy minimization as the mixed integer nonlinear programming (MINLP) problem. We then transform and solve the original problem through the RAS algorithm. For practical implementation, we further propose the fast RAS (Fast-RAS) algorithm to relax the binary integer constraints and transform the MINLP problem into the nonlinear programming (NLP) problem. The relaxed problem then can be solved by using Feasible Pump algorithm with the reduced computational complexity. We evaluate the performance of RAS and Fast-RAS algorithms via extensive simulations. The results demonstrate that the Fast-RAS algorithm can achieve up to 20% improvement of energy saving comparing with existed methods.

This paper describes efforts to develop a simulation environment for modeling the operations of an airborne surveillance aircraft. The simulated aircraft will monitor seismic and visual sensors to detect disturbances on the ground. In traditional systems, a human operator is responsible for managing all surveillance resources. The simulation environment developed in this project will allow for the evaluation of automated scheduling systems. The system described here uses an on-line optimization algorithm to schedule cameras to targets. To assess the performance of the on-line optimization algorithm, the team developed an off-line formulation of the scheduling problem to estimate an upper-bound for the optimal achievable performance. Varying both the total area defined by the user as areas of interest and those areas' corresponding priority, we assessed the intelligence-gathering capability of the system using a performance ratio. By experimentally comparing the performance ratio between the on-line algorithm's performance and the optimal achievable off-line performance, we conclude that the human operators can detriment the performance of the on-line scheduling algorithm.

New Results on Competitive Analysis of Move To Middle(MTM) List Update Algorithm using Doubly Linked List

This work presents a knowledge discovery approach through Causal Bayesian Networks for understanding the conditions under which the performance of an optimization algorithm can be affected by the characteristics of the instances of a combinatorial optimization problem (COP). We introduce a case study for the causal analysis of the performance of two state-of-the-art algorithms for the one-dimensional Bin Packing Problem (BPP). We meticulously selected the set of features associated with the parameters that define the instances of the problem. Subsequently, we evaluated the algorithmic performance on instances with distinct features. Our analysis scrutinizes both instance features and algorithm performance, aiming to identify causes influencing the performance of the algorithms. The proposed study successfully identifies specific values affecting algorithmic effectiveness and efficiency, revealing shared causes within some value ranges across both algorithms. The knowledge generated establishes a robust foundation for future research, enabling predictions of algorithmic performance, as well as the selection and design of heuristic strategies for improving the performance in the most difficult instances. The causal analysis employed in this study did not require specific configurations, making it an invaluable tool for analyzing the performance of different algorithms in other COPs.

This paper proposes a new method for probabilistic analysis of online algorithms. It is based on the notion of stochastic dominance. We develop the method for the online bin coloring problem introduced in [15]. Using methods for the stochastic comparison of Markov chains we establish the result that the performance of the online algorithm \(\textsc{GreedyFit}\) is stochastically better than the performance of the algorithm \(\textsc{OneBin}\) for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations.KeywordsMarkov ChainCompetitive RatioOnline AlgorithmStochastic DominanceMarkov Chain ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A large number of algorithms has been proposed for solving continuous optimisation problems. However, there is limited theoretical understanding of the strengths and weaknesses of most algorithms and their individual applicability. Furthermore, the performance of these algorithms is highly dependent on their control parameters, which need to be configured to achieve a peak performance. Automating the processes of selecting the most suitable algorithm and the right control parameters can help in solving continuous optimisation problems effectively and efficiently. In this paper, a simple online algorithm selector is proposed. It decides on selecting the right algorithm based on the current state of the search process to solve a given problem. Each algorithm in the portfolio of the algorithm selector competes with others and utilises the results of other algorithms to locate the global optimum. The proposed algorithm selector and the algorithms of the portfolio as stand-alone algorithms were benchmarked on the noise-free BBOB-2009 testbed. The results show that the performance of the simple algorithm selector is better than the performances of the individual algorithms in general. It was also able to solve eleven out of twenty-four functions of the test suite to the ultimate accuracy of 10-8.

We focus in this work on an aspect of online computation that is not addressed by standard competitive analysis, namely, identifying request sequences for which nontrivial online algorithms are useful versus request sequences for which all algorithms perform equally poorly. The motivations for this work are advanced system and architecture designs which allow the operating system to dynamically allocate resources to online protocols such as prefetching and caching. To utilize these features, the operating system needs to identify data streams that can benefit from more resources. Our approach in this work is based on the relation between entropy, compression, and gambling, extensively studied in information theory. It has been shown that in some settings, entropy can either fully or at least partially characterize the expected outcome of an iterative gambling game. Our goal is to study the extent to which the entropy of the input characterizes the expected performance of online algorithms for problems that arise in computer applications. We study bounds based on entropy for three classical online problems---list accessing, prefetching, and caching. Our bounds relate the performance of the best online algorithm to the entropy , a parameter intrinsic to characteristics of the request sequence. This is in contrast to the competitive ratio parameter of competitive analysis, which quantifies the performance of the online algorithm with respect to an optimal offline algorithm. For the prefetching problem, we give explicit upper and lower bounds for the performance of the best prefetching algorithm in terms of the entropy of the request sequence. In contrast, we show that the entropy of the request sequence alone does not fully capture the performance of online list accessing and caching algorithms.

Previously, extra-resource analysis has been used to argue that certain on-line algorithms are good choices for solving specific problems because these algorithms perform well with respect to the optimal off-line algorithm when given extra resources. We now introduce a new application for extra-resource analysis: deriving a qualitative divergence between off-line and on-line algorithms. We do this for the load-balancing problem, the problem of assigning a list of jobs on m identical machines to minimize the makespan, the maximum load on any machine. We analyze the worst-case performance of on-line and off-line approximation algorithms relative to performance of the optimal off-line algorithm when the approximation algorithms have k extra machines. Our main result are the following: The Longest-Processing-Time (ℒ) algorithm will produce a schedule with makespan no larger than that of the optimal off-line algorithm if ℒ has at least (4m−1) /3 machines while the optimal off-line algorithm has m machines. In contrast, no on-line algorithm can guarantee the same with any number of extra machines. Copyright © 2000 John Wiley & Sons, Ltd.

In midcourse guidance, strong constraints and dual-channel control coupling pose major challenges for trajectory optimization. To address this, this paper proposes an optimal guidance method based on terminal relaxation and range convex programming. The study first derived a range-domain dynamics model with the angle of attack and bank angle as dual control inputs, augmented with path constraints including heat flux limitations, to formulate the midcourse guidance optimization problem. A terminal relaxation strategy was then proposed to mitigate numerical infeasibility induced by rigid terminal constraints, thereby guaranteeing the solvability of successive subproblems. Through the integration of affine variable transformations and successive linearization techniques, the original nonconvex problem was systematically converted into a second-order cone programming (SOCP) formulation, with theoretical equivalence between the relaxed and original problems established under well-justified assumptions. Furthermore, a heuristic initial trajectory generation scheme was devised, and the solution was obtained via a sequential convex programming (SCP) algorithm. Numerical simulation results demonstrated that the proposed method effectively satisfies strict path constraints, successfully generates feasible midcourse guidance trajectories, and exhibits strong computational efficiency and robustness. Additionally, a systematic comparison was conducted to evaluate the impact of different interpolation methods and discretization point quantities on algorithm performance.

In this paper we study the problem of finding disjoint paths in graphs. Whereas for specific graphs many (almost) matching upper and lower bounds are known for the competitiveness of on-line path selection algorithms, much less is known about how well on-line algorithms can perform in the general setting. In several papers the expansion has been used to measure the performance of off-line and on-line algorithms in this field. We study a class of simple deterministic on-line algorithms and show that they achieve a competitive ratio that is asymptotically equal to the best possible competitive ratio that can be achieved by any deterministic on-line algorithm. For this we use a parameter caled routing number which allows more precise results than the expansion. Interestingly, our upper bound on the competitive ratio is even better than the best approximation ratio known for off-line algorithms. Furthermore, we show that a refined variant of the routing number allows to construct on-line algorithms with a competitive ratio that is for many graphs significantly below the best possible upper bound for deterministic on-line algorithms if only the routing number or expansion of a graph is known. We also show that our algorithms can be transformed into efficient algorithms for the related unsplittable flow problem.

There has been a great deal of interest recently in the relative power of on-line and off-line algorithms. An on-line algorithm receives a sequence of requests and must respond to each request as soon as it is receiveD. An off-line algorithm may wait until all requests have been received before determining its responses. One approach to evaluating an on-line algorithm is to compare its performance with that of the best possible off-line algorithm for the same problem. Thus, given a measure of profit, the performance of an on-line algorithm can be measured by the worst-case ratio of its profit to that of the optimal off-line algorithm. This general approach has been applied in a number of contexts, including data structures [SITa], bin packing [CoGaJo], graph coloring [GyLe] and the k-server problem [MaMcSI]. Here we apply it to bipartite matching and show that a simple randomized on-line algorithm achieves the best possible performance.

Boosting is an effective classifier combination method, which can improve classification performance of an unstable learning algorithm due to its theoretical performance guarantees and strong experimental results. However, the algorithm has been used mainly in batch mode, i.e., it requires the entire training set to be available at once and, in some cases, require random access to the data. Recently, Nikunj C.oza(2001) proved that some preliminary theoretical results and some empirical comparisons of the classification accuracies of online algorithms with their corresponding batch algorithms on many datasets. In this paper, we present online versions of some boosting methods that require only one pass through the training data. Specifically, we discuss how our online algorithms mirror the techniques that boosting use to generate multiple distinct base models. We also present theoretical and experimental evidence that our online algorithms succeed in this mirroring. Our online algorithms are demonstrated to be more practical with larger datasets. We also compare the online and batch algorithms experimentally in terms of accuracy .