Relative Interval Analysis of Paging Algorithms on Access Graphs

Access graphs, which have been used previously in connection with competitive analysis and relative worst order analysis to model locality of reference in paging, are considered in connection with relative interval analysis. The algorithms LRU, FIFO, FWF, and FAR are compared using the path, star, and cycle access graphs. In this model, some of the expected results are obtained. However, although LRU is found to be strictly better than FIFO on paths, it has worse performance on stars, cycles, and complete graphs, in this model. We solve an open question from [Dorrigiv, Lopez-Ortiz, Munro, 2009], obtaining tight bounds on the relationship between LRU and FIFO with relative interval analysis.Comment: IMADA-preprint-c

The Frequent Items Problem in Online Streaming under Various Performance Measures

In this paper, we strengthen the competitive analysis results obtained for a fundamental online streaming problem, the Frequent Items Problem. Additionally, we contribute with a more detailed analysis of this problem, using alternative performance measures, supplementing the insight gained from competitive analysis. The results also contribute to the general study of performance measures for online algorithms. It has long been known that competitive analysis suffers from drawbacks in certain situations, and many alternative measures have been proposed. However, more systematic comparative studies of performance measures have been initiated recently, and we continue this work, using competitive analysis, relative interval analysis, and relative worst order analysis on the Frequent Items Problem.Comment: IMADA-preprint-c

Online Bin Covering: Expectations vs. Guarantees

Bin covering is a dual version of classic bin packing. Thus, the goal is to cover as many bins as possible, where covering a bin means packing items of total size at least one in the bin. For online bin covering, competitive analysis fails to distinguish between most algorithms of interest; all "reasonable" algorithms have a competitive ratio of 1/2. Thus, in order to get a better understanding of the combinatorial difficulties in solving this problem, we turn to other performance measures, namely relative worst order, random order, and max/max analysis, as well as analyzing input with restricted or uniformly distributed item sizes. In this way, our study also supplements the ongoing systematic studies of the relative strengths of various performance measures. Two classic algorithms for online bin packing that have natural dual versions are Harmonic and Next-Fit. Even though the algorithms are quite different in nature, the dual versions are not separated by competitive analysis. We make the case that when guarantees are needed, even under restricted input sequences, dual Harmonic is preferable. In addition, we establish quite robust theoretical results showing that if items come from a uniform distribution or even if just the ordering of items is uniformly random, then dual Next-Fit is the right choice.Comment: IMADA-preprint-c

zCap: a zero configuration adaptive paging and mobility management mechanism

Today, cellular networks rely on fixed collections of cells (tracking areas) for user equipment localisation. Locating users within these areas involves broadcast search (paging), which consumes radio bandwidth but reduces the user equipment signalling required for mobility management. Tracking areas are today manually configured, hard to adapt to local mobility and influence the load on several key resources in the network. We propose a decentralised and self-adaptive approach to mobility management based on a probabilistic model of local mobility. By estimating the parameters of this model from observations of user mobility collected online, we obtain a dynamic model from which we construct local neighbourhoods of cells where we are most likely to locate user equipment. We propose to replace the static tracking areas of current systems with neighbourhoods local to each cell. The model is also used to derive a multi-phase paging scheme, where the division of neighbourhood cells into consecutive phases balances response times and paging cost. The complete mechanism requires no manual tracking area configuration and performs localisation efficiently in terms of signalling and response times. Detailed simulations show that significant potential gains in localisation effi- ciency are possible while eliminating manual configuration of mobility management parameters. Variants of the proposal can be implemented within current (LTE) standards

Learning-Augmented Weighted Paging

We consider a natural semi-online model for weighted paging, where at any time the algorithm is given predictions, possibly with errors, about the next arrival of each page. The model is inspired by Belady's classic optimal offline algorithm for unweighted paging, and extends the recently studied model for learning-augmented paging (Lykouris and Vassilvitskii, 2018) to the weighted setting. For the case of perfect predictions, we provide an $\ell$-competitive deterministic and an $O(\log \ell)$-competitive randomized algorithm, where $\ell$ is the number of distinct weight classes. Both these bounds are tight, and imply an $O(\log W)$- and $O(\log \log W)$-competitive ratio, respectively, when the page weights lie between $1$ and $W$. Previously, it was not known how to use these predictions in the weighted setting and only bounds of $k$ and $O(\log k)$ were known, where $k$ is the cache size. Our results also generalize to the interleaved paging setting and to the case of imperfect predictions, with the competitive ratios degrading smoothly from $O(\ell)$ and $O(\log \ell)$ to $O(k)$ and $O(\log k)$, respectively, as the prediction error increases. Our results are based on several insights on structural properties of Belady's algorithm and the sequence of page arrival predictions, and novel potential functions that incorporate these predictions. For the case of unweighted paging, the results imply a very simple potential function based proof of the optimality of Belady's algorithm, which may be of independent interest

Algorithm-Level Optimizations for Scalable Parallel Graph Processing

Efficiently processing large graphs is challenging, since parallel graph algorithms suffer from poor scalability and performance due to many factors, including heavy communication and load-imbalance. Furthermore, it is difficult to express graph algorithms, as users need to understand and effectively utilize the underlying execution of the algorithm on the distributed system. The performance of graph algorithms depends not only on the characteristics of the system (such as latency, available RAM, etc.), but also on the characteristics of the input graph (small-world scalefree, mesh, long-diameter, etc.), and characteristics of the algorithm (sparse computation vs. dense communication). The best execution strategy, therefore, often heavily depends on the combination of input graph, system and algorithm. Fine-grained expression exposes maximum parallelism in the algorithm and allows the user to concentrate on a single vertex, making it easier to express parallel graph algorithms. However, this often loses information about the machine, making it difficult to extract performance and scalability from fine-grained algorithms. To address these issues, we present a model for expressing parallel graph algorithms using a fine-grained expression. Our model decouples the algorithm-writer from the underlying details of the system, graph, and execution and tuning of the algorithm. We also present various graph paradigms that optimize the execution of graph algorithms for various types of input graphs and systems. We show our model is general enough to allow graph algorithms to use the various graph paradigms for the best/fastest execution, and demonstrate good performance and scalability for various different graphs, algorithms, and systems to 100,000+ cores

Paging with Dynamic Memory Capacity

We study a generalization of the classic paging problem that allows the amount of available memory to vary over time - capturing a fundamental property of many modern computing realities, from cloud computing to multi-core and energy-optimized processors. It turns out that good performance in the "classic" case provides no performance guarantees when memory capacity fluctuates: roughly speaking, moving from static to dynamic capacity can mean the difference between optimality within a factor 2 in space and time, and suboptimality by an arbitrarily large factor. More precisely, adopting the competitive analysis framework, we show that some online paging algorithms, despite having an optimal (h,k)-competitive ratio when capacity remains constant, are not (3,k)-competitive for any arbitrarily large k in the presence of minimal capacity fluctuations. In this light it is surprising that several classic paging algorithms perform remarkably well even if memory capacity changes adversarially - in fact, even without taking those changes into explicit account! In particular, we prove that LFD still achieves the minimum number of faults, and that several classic online algorithms such as LRU have a "dynamic" (h,k)-competitive ratio that is the best one can achieve without knowledge of future page requests, even if one had perfect knowledge of future capacity fluctuations. Thus, with careful management, knowing/predicting future memory resources appears far less crucial to performance than knowing/predicting future data accesses. We characterize the optimal "dynamic" (h,k)-competitive ratio exactly, and show it has a somewhat complex expression that is almost but not quite equal to the "classic" ratio k/(k-h+1), thus proving a strict if minuscule separation between online paging performance achievable in the presence or absence of capacity fluctuations

An accurate prefetching policy for object oriented systems

PhD ThesisIn the latest high-performance computers, there is a growing requirement for accurate prefetching(AP) methodologies for advanced object management schemes in virtual memory and migration systems. The major issue for achieving this goal is that of finding a simple way of accurately predicting the objects that will be referenced in the near future and to group them so as to allow them to be fetched same time. The basic notion of AP involves building a relationship for logically grouping related objects and prefetching them, rather than using their physical grouping and it relies on demand fetching such as is done in existing restructuring or grouping schemes. By this, AP tries to overcome some of the shortcomings posed by physical grouping methods. Prefetching also makes use of the properties of object oriented languages to build inter and intra object relationships as a means of logical grouping. This thesis describes how this relationship can be established at compile time and how it can be used for accurate object prefetching in virtual memory systems. In addition, AP performs control flow and data dependency analysis to reinforce the relationships and to find the dependencies of a program. The user program is decomposed into prefetching blocks which contain all the information needed for block prefetching such as long branches and function calls at major branch points. The proposed prefetching scheme is implemented by extending a C++ compiler and evaluated on a virtual memory simulator. The results show a significant reduction both in the number of page fault and memory pollution. In particular, AP can suppress many page faults that occur during transition phases which are unmanageable by other ways of fetching. AP can be applied to a local and distributed virtual memory system so as to reduce the fault rate by fetching groups of objects at the same time and consequently lessening operating system overheads.British Counci