An adaptive computation maintains the relationship between its input and output as the input changes. Although various techniques for adaptive computing have been proposed, they remain limited in their scope of applicability. We propose a general mechanism for adaptive computing that enables one to make any purely-functional program adaptive. We show

Self-adjusting computation uses a combination of dynamic dependence graphs and memoization to efficiently update the output of a program as the input changes incrementally or dynamically over time. Related work showed various theoretical results, indicating that the approach can be effective for a reasonably broad range of applications. In this article, we describe algorithms and implementation techniques to realize self-adjusting computation and present an experimental evaluation of the proposed approach on a variety of applications, ranging from simple list primitives to more sophisticated computational geometry algorithms. The results of the experiments show that the approach is effective in practice, often offering orders of magnitude speedup from recomputing the output from scratch. We believe this is the first experimental evidence that incremental computation of any type is effective in practice for a reasonably broad set of applications.

Self-adjusting computation offers a language-centric approach to writing programs that can automatically respond to modifications to their data (e.g., inputs). Except for several domain-specific implementations, however, all previous implementations of self-adjusting computation assume mostly functional, higher-order languages such as Standard ML. Prior to this work, it was not known if self-adjusting computation can be made to work with low-level, imperative languages such as C without placing undue burden on the programmer. We describe the design and implementation of CEAL: a C-based language for self-adjusting computation. The language is fully general and extends C with a small number of primitives to enable writing self-adjusting programs in a style similar to conventional C programs. We present efficient compilation techniques for translating CEAL programs into C that can be compiled with existing C compilers using primitives supplied by a run-time library for self-adjusting computation. We implement the proposed compiler and evaluate its effectiveness. Our experiments show that CEAL is effective in practice: compiled self-adjusting programs respond to small modifications to their data by orders of magnitude faster than recomputing from scratch while slowing down a from-scratch run by a moderate constant factor. Compared to previous work, we

Abstract. This paper presents a semantics of self-adjusting computation and proves that the semantics is correct and consistent. The semantics integrates change propagation with the classic idea of memoization to enable reuse of computations under mutation to memory. During evaluation, reuse of a computation via memoization triggers a change propagation that adjusts the reused computation to reflect the mutated memory. Since the semantics combines memoization and change-propagation, it involves both non-determinism and mutation. Our consistency theorem states that the non-determinism is not harmful: any two evaluations of the same program starting at the same state yield the same result. Our correctness theorem states that mutation is not harmful: self-adjusting programs are consistent with purely functional programming. We formalized the semantics and its meta-theory in the LF logical framework and machine-checked the proofs in Twelf. 1

Many algorithms and applications involve repeatedly solving variations of the same inference problem; for example we may want to introduce new evidence to the model or perform updates to conditional dependencies. The goal of adaptive inference is to take advantage of what is preserved in the model and perform inference more rapidly than from scratch. In this paper, we describe techniques for adaptive inference on general graphs that support marginal computation and updates to the conditional probabilities and dependencies in logarithmic time. We give experimental results for an implementation of our algorithm, and demonstrate its potential performance benefit in the study of protein structure. 1

The dynamic trees problem is that of maintaining a forest that changes over time through edge insertions and deletions. We can associate data with vertices or edges and manip-ulate this data, individually or in bulk, with operations that deal with whole paths or trees. Efficient solutions to this problem have numerous applications, particularly in algo-rithms for network flows and dynamic graphs in general. Several data structures capable of logarithmic-time dynamic tree operations have been proposed. The first was Sleator and Tarjan’s ST-tree, which represents a partition of the tree into paths. Although reasonably fast in practice, adapting ST-trees to different applications is nontrivial. Frederickson’s topology trees, Alstrup et al.’s top trees, and Acar et al.’s RC-trees are based on tree contractions: they progressively combine vertices or edges to obtain a hierarchical represen-tation of the tree. This approach is more flexible in theory, but all known implementations assume the trees have bounded degree; arbitrary trees are supported only after ternar-ization. This thesis shows how these two approaches can be combined (with very little overhead) to produce a data structure that is at least as generic as any other, very easy to

Abstract. Dynamic tree data structures maintain forests that change over time through edge insertions and deletions. Besides maintaining connectivity information in logarithmic time, they can support aggregation of information over paths, trees, or both. We perform an experimental comparison of several versions of dynamic trees: ST-trees, ET-trees, RC-trees, and two variants of top trees (self-adjusting and worst-case). We quantify their strengths and weaknesses through tests with various workloads, most stemming from practical applications. We observe that a simple, linear-time implementation is remarkably fast for graphs of small diameter, and that worst-case and randomized data structures are best when queries are very frequent. The best overall performance, however, is achieved by self-adjusting ST-trees. 1

Abstract. In self-adjusting computation, programs respond automatically and efficiently to modifications to their data by tracking the dynamic data dependences of the computation and incrementally updating the output as needed. In this tutorial, we describe the self-adjustingcomputation model and present the language ∆ML (Delta ML) for writing self-adjusting programs. 1

Motivated by stochastic systems in which observed evidence and conditional dependencies between states of the network change over time, and certain quantities of interest (marginal distributions, likelihood estimates etc.) must be updated, we study the problem of adaptive inference in tree-structured Bayesian networks. We describe an algorithm for adaptive inference that handles a broad range of changes to the network and is able to maintain marginal distributions, MAP estimates, and data likelihoods in all expected logarithmic time. We give an implementation of our algorithm and provide experiments that show that the algorithm can yield up to two orders of magnitude speedups on answering queries and responding to dynamic changes over the sum-product algorithm. 1

This papers proposes techniques for writing self-adjusting programs that can adjust to any change to their data (e.g., inputs, decisions made during the computation) etc. We show that the techniques are e#cient by considering a number of applications including several sorting algorithms, and the Graham Scan, and the quick hull algorithm for computing convex hulls. We show that the techniques are flexible by showing that self-adjusting programs can be trivially transformed into a kinetic programs that maintain their property as their input move continuously. We show that the techniques are practical by implementing a Standard ML library for kinetic data structures and applying the library to kinetic convex hulls. We show that the kinetic programs written with the library are more than an order of magnitude faster than recomputing from scratch. These results rely on a combination of memoization and dynamic dependence graphs. We show that the combination is sound by presenting a semantics based on abstraction of memoization via an oracle.