Self-organizing Lists Research Articles

A Novel Framework for Self-Organizing Lists in Environments with Locality of Reference: Lists-on-Lists

We examine the problem of self-organizing linear search lists, which are lists that react to queries received from an environment by running a heuristic to reorganize the records in order to minimize the search cost. In particular, we are concerned with environments with the locality of reference phenomenon, when the queries exhibit a probabilistic dependence between themselves. We introduce a novel list organization framework that we call Lists-on-Lists (LOL), which regards the list as a set of sublists that are manageable in the same way that individual records are. An LOL organization involves a reorganization operation on the accessed record level, as well as another on the sublist which it belongs to (the record's context). We show that it is beneficial to consider the reorganization of the context together with the accessed record, since other records within the context are likely to be accessed in the near future. With the aid of a learning automaton-based partitioning algorithm, we demonstrate that we can accurately classify the different contexts of the sublist. To the best of our knowledge, both the concept of reorganizing the list 'hierarchically' using such a two-step LOL process, and the application of stochastic learning to this problem are new to the field. Indeed, while the costs involved to achieve these enhancements are almost of the same order as that which achieves basic list-organizing, using this framework, we were able to empirically achieve asymptotic search costs that are significantly superior to (sometimes even an order of magnitude better than) the Move-To-Front heuristic, widely acknowledged as the best algorithm for such environments.

Adaptive low-power address encoding techniques using self-organizing lists

Off-chip bus transitions are a major source of power dissipation for embedded systems. In this paper, new adaptive encoding schemes are proposed that significantly reduce transition activity on data and multiplexed address buses. These adaptive techniques are based on self-organizing lists to achieve reduction in transition activity by exploiting the spatial and temporal locality of the addresses. Also the proposed techniques do not require any extra bit lines and have minimal delay overhead. The techniques are evaluated for efficiency using a wide variety of application programs including SPEC 95 benchmark set. Unlike previous approaches that focus on instruction address buses, experiments demonstrate significant reduction in transition activity of up to 54% in data address buses and up to 59% in multiplexed address buses. The average reductions are twice those obtained using current schemes on a data address bus and more than twice those obtained on a multiplexed address bus.

The move-to-partner rule for self-organizing task allocation on a linear array

The well-known Move-to-Front rule for self-organizing lists is modified to a so-called Move-to-Partner rule for dynamic task allocation on a chain of processors. We enable an analysis of the sequence of expected communication costs by reducing their computation to that of three-dimensional arrays of certain probabilities, for which a recursion formula and an asymptotic expansion can be given. The costs depend on the underlying communication profile; two types of such profiles are investigated in more detail, namely a two-dimensional version of Zipf's law, and profiles based on a class structure of tasks. In the considered cases, the Move-to-Partner rule effects fast convergence to a stationary state, but comparably high expected stationary costs.

Performance of the move-to-front algorithm with Markov-modulated request sequences

We study the classical move-to-front (MTF) algorithm for self-organizing lists within the Markov-modulated request (MMR) model. Such models are useful when list accesses are generated within a relatively small set of modes, with the request sequences in each mode being i.i.d. These modes are often called localities of reference and are known to exist in such applications as traffic streams of Ethernet or ATM networks and the locus of control or data accesses of executing computer programs. Our main results are explicit formulas for the mean and variance of the search-cost, the number of accesses required to find a given list element. By adjusting the number of modes, one can use the MMR methodology to trade off the quality of an approximation with the computational effort it requires. Thus, our results provide a useful new tool for evaluating the MTF rule in linear-search applications with correlated request sequences. We illustrate the computations with several examples.

Limits and rates of convergence for the distribution of search cost under the move-to-front rule

We derive upper and lower bounds on total variation distance to stationarity for the distribution of search cost under the move-to-front (MTF) rule for self-organizing lists with i.i.d. record requests. These enable us to obtain sharp rates of convergence for several standard examples of weights, including Zipf's law and geometric weights, as the length of the list becomes large. The upper bound also shows that a number of moves of the order of the length of the list is uniformly sufficient for near-stationarity over all choices of weights. Concerning the stationary search cost distribution itself, we use a representation obtained by considering the continuized MTF Markov chain to derive, for each of the standard examples, the asymptotic distribution for long lists.

An exact formula for the move-to-front rule for self-organizing lists

A collection of items (e.g., books), each with an associated weight (or popularity), is arranged in a row. At each unit of time an item is removed with probability proportional to its weight and replaced at the left end of the row. Thismove-to-front rule gives a Markov chain on permutations often known as theTsetlin library. We derive an exact and tractable formula for the probability of any permutation after any number of moves. From the formula we read off previously studied quantities of interest associated with the chain, such as the stationary distribution and eigenvalues. Measuring discrepancy from stationarity by separation, we use the formula to find the initial arrangement giving the slowest convergence to stationarity. The time to stationarity in this case is a convolution of geometric random variables which we analyze for three natural choices of weights. We also assess the time required for an important functional, namely, expected search cost, to approach its stationary value.

On the Markov Chain for the Move-to-Root Rule for Binary Search Trees

The move-to-root (MTR) heuristic is a self-organizing rule that attempts to keep a binary search tree in near-optimal form. It is a tree analogue of the move-to-front (MTF) scheme for self-organizing lists. Both heuristics can be modeled as Markov chains. We show that the MTR chain can be derived by lumping the MTF chain and give exact formulas for the transition probabilities and stationary distribution for MTR. We also derive the eigenvalues and their multiplicities for MTR.

Rates of Convergence for the Move-to-Root Markov Chain for Binary Search Trees

The move-to-root heuristic is a self-organizing rule that attempts to keep a binary search tree in near-optimal form. It is a tree analogue of the move-to-front scheme (also known as the weighted random-to-top card shuffle or Tsetlin library) for self-organizing lists. We study convergence of the move-to-root Markov chain to its stationary distribution and show that move-to-root converges two to four times faster than move-to-front for many examples. We also discuss asymptotics for expected search cost. For equal weights, $\operatorname{cn}/\ln n$ steps are necessary and sufficient to drive the maximum relative error to 0.

Systolic self-organizing lists under transpose

Systolic array architectures for self-organizing linear lists under the transpose update heuristic are presented. The first model has linear delay and restricts input on every other system cycle. The second system combines a systolic array with trees to provide logarithmic delay and input on every clock cycle. These preliminary designs can be the basis of hardware used to achieve high-speed lossless data compression for data communication and storage. On large files (greater than 40 kilobytes), our designs provide better compression than other systolic list compression schemes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Self-Organizing Doubly-Linked Lists

In this paper, we study the problem of maintaining a doubly-linked list (DLL) in approximately optimal order, with respect to the mean search time. We study two types of DLL reorganization strategies. Move-To-End (MTE) [12] and SWAP [14] are two memoryless DLL heuristics obtained from natural extensions of the well-known singly-linked-list (SLL) heuristics, move-to-front and transposition, respectively. We first derive a general sufficient condition which permits comparison of any two DLL heuristics. We use this condition as a guideline to identify families of access distributions for which SWAP yields a lower expected cost than the MTE. We have also presented an absorbing DLL heuristic. The strategy requires one additional memory location and is analogous to the scheme presented in [15]. The reorganization is achieved by moving each element exactly once to its final position in the reorganized list. The scheme is stochastically absorbing and it is shown to be optimal for a restricted family of distributions. Thus, for these distributions, the probability of the scheme converging to the optimal list order can be made as close to unity as desired.

Self-organizing lists and independent references: A statistical synergy

Let R 1,…, R n be a linear list of n elements. We assume the independent reference model, with a fixed but unknown access probability vector. We survey briefly the problem of reorganizing the list dynamically, on the basis of accrued references, with the objective of minimizing the expected access cost. The counter scheme (CS) is known to be asymptotically optimal for this purpose. The paper explores the CS, with the aim of reducing its storage requirements. We start with a detailed exposition of its cost function and then point out that it interacts with the access model to produce some remarkable synergistic effects. These make it possible to use very effective “truncated versions” of the CS, which have very modest space requirements. The versions we consider are: (i) the “limited-counters scheme”, which bounds each of the frequency counters to a maximal value c; (ii) the original CS with a bound on the number of references during which the scheme is active. The bound is chosen so as to achieve a desired level of performance compared with the optimal policy.

Image Vector Quantizer Using Self-Organizing List

従来の画像のベクトル量子化法では, 量子化演算量とコードブックメモリー量との制約により, ブロックサイズの拡大が困難となり, 充分な圧縮率が得られていない.本論文では, 自己組織型リストをインデックスの符号化やコードブックの管理に導入することによって, ブロック間の相関や冗長性を符号化の際に利用する4種類の新たなベクトル量子化法を提案している.すなわち, まず, ベクトル量子化インデックスを自己組織型リストを用いて符号化する方式と, 量子化出力ベクトルの探索および符号化に自己組織型リストを用いた自己組織ベクトル量子化法とを基本方式として提案した.さらに, 自己組織ベクトル量子化法を発展させた方式として, DPCM符号化によるコードワードの追加登録機能を付加した方式と, 低次元のコードワードを複数連結して高次元のコードワードを生成する機能を導入した方式とを提案した.また, これらの方式の有用性をシミュレーションにより確認している.