Topology Matters: Smoothed Competitiveness of Metrical Task Systems

We consider online problems that can be modeled as metrical task systems: An online algorithm resides in a graph of n nodes and may move in this graph at a cost equal to the distance. The algorithm has to service a sequence of tasks that arrive over time; each task specifies for each node a request cost that is incurred if the algorithm services the task in this particular node. The objective is to minimize the total request plus travel cost. Borodin, Linial and Saks gave a deterministic work function algorithm (WFA) for metrical task systems having a tight competitive ratio of 2n-1. We present a smoothed competitive analysis of WFA. Given an adversarial task sequence, we add some random noise to the request costs and analyze the competitive ratio of WFA on the perturbed sequence. We prove upper and matching lower bounds. Our analysis reveals that the smoothed competitive ratio of WFA is much better than its (worst case) competitive ratio and that it depends on several topological parameters of the graph underlying the metric, such as maximum degree, diameter, etc. For example, already for moderate perturbations, the smoothed competitive ratio of WFA is O(log(n)) on a clique and O(sqrt{n}) on a line. We also provide the first average case analysis of WFA. For a large class of probability distributions, we prove that WFA has O(log(D)) expected competitive ratio, where D is the maximum degree of the underlying graph

Semi-online Scheduling with Lookahead

The knowledge of future partial information in the form of a lookahead to design efficient online algorithms is a theoretically-efficient and realistic approach to solving computational problems. Design and analysis of semi-online algorithms with extra-piece-of-information (EPI) as a new input parameter has gained the attention of the theoretical computer science community in the last couple of decades. Though competitive analysis is a pessimistic worst-case performance measure to analyze online algorithms, it has immense theoretical value in developing the foundation and advancing the state-of-the-art contributions in online and semi-online scheduling. In this paper, we study and explore the impact of lookahead as an EPI in the context of online scheduling in identical machine frameworks. We introduce a $k$-lookahead model and design improved competitive semi-online algorithms. For a $2$-identical machine setting, we prove a lower bound of $\frac{4}{3}$ and design an optimal algorithm with a matching upper bound of $\frac{4}{3}$ on the competitive ratio. For a $3$-identical machine setting, we show a lower bound of $\frac{15}{11}$ and design a $\frac{16}{11}$-competitive improved semi-online algorithm.Comment: 14 pages, 1 figur

On the List Update Problem with Advice

We study the online list update problem under the advice model of computation. Under this model, an online algorithm receives partial information about the unknown parts of the input in the form of some bits of advice generated by a benevolent offline oracle. We show that advice of linear size is required and sufficient for a deterministic algorithm to achieve an optimal solution or even a competitive ratio better than $15/14$. On the other hand, we show that surprisingly two bits of advice are sufficient to break the lower bound of $2$ on the competitive ratio of deterministic online algorithms and achieve a deterministic algorithm with a competitive ratio of $5/3$. In this upper-bound argument, the bits of advice determine the algorithm with smaller cost among three classical online algorithms, TIMESTAMP and two members of the MTF2 family of algorithms. We also show that MTF2 algorithms are $2.5$-competitive

Adaptive Physical Design for Curated Archives

We introduce AdaptPD, an automated physical design tool that improves database performance by continuously monitoring changes in the workload and adapting the physical design to suit the incoming workload. Current physical design tools are offline and require specification of a representative workload. AdaptPD is “always on” and incorporates online algorithms which profile the incoming workload to calculate the relative benefit of transitioning to an alternative design. Efficient query and transition cost estimation modules allow AdaptPD to quickly decide between various design configurations. We evaluate AdaptPD with the SkyServer Astronomy database using queries submitted by SkyServer’s users. Experiments show that AdaptPD adapts to changes in the workload, improves query performance substantially over offline tools, and introduces minor computational overhead

Exact distributional analysis of online algorithms with lookahead

In online optimization, input data is revealed sequentially. Optimization problems in practice often exhibit this type of information disclosure as opposed to standard offline optimization where all information is known in advance. We analyze the performance of algorithms for online optimization with lookahead using a holistic distributional approach. To this end, we first introduce the performance measurement method of counting distribution functions. Then, we derive analytical expressions for the counting distribution functions of the objective value and the performance ratio in elementary cases of the online bin packing and the online traveling salesman problem. For bin packing, we also establish a relation between algorithm processing and the Catalan numbers. The paper shows that an exact analysis is strongly interconnected to the combinatorial structure of the problem and algorithm under consideration. Results further indicate that the value of lookahead heavily relies on the problem itself. The analysis also shows that exact distributional analysis could be used in order to discover key effects and identify related root causes in relatively simple problem settings. These insights can then be transferred to the analysis of more complex settings where the introduced performance measurement approach has to be used on an approximative basis (e.g., in a simulation-based optimization)

Samoupravující seznamy

Samoupravující seznamy Samoupravující seznamy jsou datové struktury sloužící k rychlému vyhledávání za předpokladu, že některé prvky v nich uložené jsou vyhledávány častěji než jiné, přičemž pravděpodobnosti přístupu k jednotlivým prvkům obecně nejsou předem známy. Efektivnějšího vyhledávání je dosaženo použitím různých permutačních pravidel, která průběžně mění uspořádání seznamu tak, aby častěji vyhledávané prvky byly blíže k jeho začátku. V této práci je uveden přehled známých algoritmů pro řešení tohoto problému (s uvedením teoretických výsledků o jejich složitosti, jsou-li známy) a experimentální studie o jejich chování (s využitím vlastních nebo volně dostupných implementací a programových prostředků pro generování vstupních dat, testování algoritmů a zpracování výsledků experimentů).Self-organizing linear lists Self-organizing linear lists are data structures for fast search, provided that certain elements stored in them are searched more frequently than others, while the probability of access to individual elements is generally not known in advance. Efficient search is achieved using different permutation rules that keep changing the list structure so that the more frequently searched elements are closer to the beginning. This thesis gives an overview of known algorithms for solving this problem (with the theoretical results about their complexity, if they are known), and experimental study of their behavior (using its own or freely available implementations and software for generating input data, testing algorithms and processing the results of experiments).Department of Distributed and Dependable SystemsKatedra distribuovaných a spolehlivých systémůFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Lookahead scheduling in a real-time context: Models, algorithms, and analysis

Our research considers job scheduling, a special type of resource assignment problem. For example, at a cross-docking facility trucks must be assigned to doors where they will be unloaded. The cargo on each truck has various destinations within the facility, and the unloading time for a truck is dependent on the distance from the assigned door to these destinations. The goal is to assign the trucks to doors while minimizing the amount of time to unload all trucks.;We study scheduling algorithms for problems like the cross-docking example that are different from traditional algorithms in two ways. First, we utilize real-time, where the algorithm executes at the same time as when the jobs are handled. Because the time used by the algorithm to make decisions cannot be used to complete a job, these decisions must be made quickly Second, our algorithms utilize lookahead, or partial knowledge of jobs that will arrive in the future.;The three goals of this research were to demonstrate that lookahead algorithms can be implemented effectively in a real-time context, to measure the amount of improvement gained by utilizing lookahead, and to explore the conditions in which lookahead is beneficial.;We present a model suitable for representing problems that include lookahead in a real-time context. Using this model, we develop lookahead algorithms for two important job scheduling systems and argue that these algorithms make decisions efficiently. We then study the performance of lookahead algorithms using mathematical analysis and simulation.;Our results provide a detailed picture of the behavior of lookahead algorithms in a real-time context. Our analytical study shows that lookahead algorithms produce schedules that are significantly better than those without lookahead. We also found that utilizing Lookahead-1, or knowledge of the next arriving job, produces substantial improvement while requiring the least effort to design. When more lookahead information is used, the solutions are better, but the amount of improvement is not significantly larger than a Lookahead-1 algorithm. Further, algorithms utilizing more lookahead are more complex to design, implement, and analyze. We conclude that Lookahead-1 algorithms are the best balance between improvement and design effort