AFSCN scheduling: How the problem and solution have evolved

The Air Force Satellite Control Network (AFSCN) coordinates communications to more than 100 satellites via nine ground stations positioned around the globe. Customers request an antenna at a ground station for a specific time window along with possible alternative slots. Typically, 500 requests per day result in more than 100 conflicts, which are requests that cannot be satisfied because other tasks need the same slot. Scheduling access requests is referred to as the Satellite Range Scheduling Problem (SRSP).This paper presents an overview of three key issues: (1) how has the problem changed over the last 10 years, (2) what algorithms work best and (3) what objective function is appropriate for AFSCN. We compared data sets from 1992 and from 2002/2003 and found significant differences in the problems. Our evaluation of solutions focuses on three algorithms: local search, Gooley’s algorithm from AFIT, and the Genitor genetic algorithm. It can be shown that local search (and therefore metaheuristics based on local search) fail to compete with Gooley’s algorithm and Genitor. Finally, while all prior work on AFSCN minimizes request conflicts, we explore an alternative objective function. Because human schedulers must eventually schedule all requests, it might be better to optimize schedules for “repairability”. Our results suggest that minimizing schedule overlaps makes it easier to fit larger requests into the schedule.     

The k-Client Problem

Virtually all previous research in online algorithms has focused on single-threaded systems where only a single sequence of requests compete for system resources. To model multithreaded online systems, we define and analyze the k-client problem, a dual of the well-studied k-server problem. In the basic k-client problem, there is a single server and k clients, each of which generates a sequence of requests for service in a metric space. The crux of the problem is deciding which client's request the single server should service rather than which server should be used to service the current request. We also consider variations where requests have nonzero processing times and where there are multiple servers as well as multiple clients.We evaluate the performance of algorithms using several cost functions including maximum completion time and average completion time. Two of the main results we derive are tight bounds on the performance of several commonly studied disk scheduling algorithms and lower bounds of on the competitive ratio of any online algorithm for the maximum completion time and average completion time cost functions when k is a power of 2. Most of our results are essentially identical for the maximum completion time and average completion time cost functions.     

Comparison of policies in dynamic routing problems

We consider a company that has to satisfy customers' pick-up requests arriving over time every day. The overall objective of the company is to serve as many requests as possible at a minimum operational cost. When organizing its business the company has to fix some features of the service that may affect both service quality and operational costs. Some of these features concern the time a request is taken into account to plan its service, the associated deadline and the way requests are managed when the system is overloaded. In this paper we analyse several policies that can be implemented by the management of a carrier company in a multi-period context. For example, a company might reject all the requests that cannot be feasibly scheduled or accept all the requests and rely on a backup service in order to serve requests that are difficult to handle. Another interesting issue considered in this paper is the impact of collaborative service where two or more carrier companies, with their own customers, decide to share customers in order to optimize the overall costs. We set up a general framework to allow comparison of alternative service policies. Extensive computational results evaluating the number of lost requests and the distance travelled provide interesting insights.     

The Distributedk-Server Problem—A Competitive Distributed Translator fork-Server Algorithms

We consider thek-server problem23in a distributed setting. Given a network ofnprocessors andkidentical mobile servers, requests for service appear at the processors and a server must reach the request point. In addition to modeling problems in computer networks wherekidentical mobile resources are shared by the processors of the network, this models a realistic situation where the transfer of information is costly and there is no central control that governs the behavior of servers that move around to satisfy requests for service. We give a general translator to transform any deterministic global-control competitivek-server algorithm into a distributed competitive one. As consequences we get poly(k)-competitive distributed algorithms for the line, trees, and the ring. In contrast to the global-control case where there arek-server algorithms with competitive ratio that depends solely onk, we have a lower bound of Ω(max{k, (1/D) ·(log n/log log n)}) on the competitive ratio of any distributedk-server algorithm, where 1/Dis the ratio between the cost to transmit a message and the cost to move a server over the same distance. We also give a distributed version of the Harmonic randomizedk-server algorithm.     

A generic auction algorithm for the minimum cost network flow problem

In this paper we broadly generalize the assignment auction algorithm to solve linear minimum cost network flow problems. We introduce a generic algorithm, which contains as special cases a number of known algorithms, including the -relaxation method, and the auction algorithm for assignment and for transportation problems. The generic algorithm can serve as a broadly useful framework for the development and the complexity analysis of specialized auction algorithms that exploit the structure of particular network problems. Using this framework, we develop and analyze two new algorithms, an algorithm for general minimum cost flow problems, called network auction, and an algorithm for thek node-disjoint shortest path problem.     

Applications of random sampling to on-line algorithms in computational geometry

This paper presents a general framework for the design and randomized analysis of geometric algorithms. These algorithms are on-line and the framework provides general bounds for their expected space and time complexities when averaging over all permutations of the input data. The method is general and can be applied to various geometric problems. The power of the technique is illustrated by new efficient on-line algorithms for constructing convex hulls and Voronoi diagrams in any dimension, Voronoi diagrams of line segments in the plane, arrangements of curves in the plane, and others. This work has been supported in part by the ESPRIT Basic Research Action Nr. 3075 (ALCOM).     

On Dynamic Algorithms for Algebraic Problems

In this paper, we examine the problem of incrementally evaluating algebraic functions. In particular, iff(x₁,x₂,…,x_n) = (y₁, y₂,…,y_m) is an algebraic problem, we consider answering on-line requests of the form “change inputx_ito valuev” or “what is the value of outputy_j?” We first present lower bounds for some simply stated algebraic problems such as multipoint polynomial evaluation, polynomial reciprocal, and extended polynomial GCD, proving an Ω(n) lower bound for the incremental evaluation of these functions. In addition, we prove two time-space trade-off theorems that apply to incremental algorithms for almost all algebraic functions. We then derive several general-purpose algorithm design techniques and apply them to several fundamental algebraic problems. For example, we give antime per request algorithm for incremental DFT. We also present a design technique for serving incremental requests using a parallel machine, giving a choice of either optimal work with respect to the sequential incremental algorithm or superfast algorithms withO(log log n) time per request with a sublinear number of processors.     

Competitive Analysis for the On-line Truck Transportation Problem

In this paper, the on-line k-truck transportation problem (k-OLTTP) whose objects are to be transported between the vertices of a given graph on which there are k mobile trucks to be scheduled is proposed. It is motivated by the research concerning on-line k-truck problem and on-line transportation problem. The goal is to minimize the makespan which is consumed to complete some on-line request sequence. Some preliminary knowledge is introduced and the model of k-OLTTP is established firstly. Two versions of a special case of k-OLTTP, namely 1-OLTTP, have been studied and some results are obtained. For the first version, Open-1-OLTTP, a lower bound of competitive ratio 2 is presented and two optimal on-line algorithms, Reschedule Strategy (RS) and Lay Over Strategy (LOS) respectively, are analyzed. For the second version, Close-1-OLTTP, a lower bound of competitive ratio , where θ is the ratio between the time consumed by the loaded truck and the empty truck to travel the same distance, is also developed and on-line algorithms RS and LOS are proved to have competitive ratio 2. Finally, some interesting remarks concerning OLTTP and its future research are discussed.     

极小化总加权完工时间的Dial-a-Ride问题的在线随机算法

讨论一般度量空间上带单服务器的极小化总加权完工时间在线Dial-a-Ride问题.通过应用贪婪区间的技巧,提出了一个一般在线随机算法.根据这个算法,对于容量为1或者任意容量的一般度量空间上的在线Dial-a-Ride问题能得到一个竞争比为(2+√2)/ln(1+√2)的在线随机算法,这个算法不仅具有当前最好的竞争比,而且也改进了Krumke等人的结果.     

On the on-line maintenance scheduling problem

A machine instantly serves requests but needs to undergo maintenance after serving a maximum of L requests. We want to maximize the number of requests served. In the on-line version, we prove that serving L requests before placing a maintenance is 0.5-competitive and is best possible for deterministic algorithms. We describe a 0.585-competitive randomized algorithm and show an upper bound of \(2L/(3L-1)\). We also analyze the empirical performance of various on-line algorithms on specific arrival distributions.