Related papers: Analysis of Logarithmic Amortised Complexity
Planning is a notoriously difficult computational problem of high worst-case complexity. Researchers have been investing significant efforts to develop heuristics or restrictions to make planning practically feasible. Case-based planning is…
We develop a rounding method based on random walks in polytopes, which leads to improved approximation algorithms and integrality gaps for several assignment problems that arise in resource allocation and scheduling. In particular, it…
Organisms adapt to volatile environments by integrating sensory information with internal memory, yet their information processing is constrained by resource limitations. Such limitations can fundamentally alter optimal estimation…
In earlier work, we developed an approach for automatic complexity analysis of integer programs, based on an alternating modular inference of upper runtime and size bounds for program parts. In this paper, we show how recent techniques to…
Autoregressive large language models (LLMs) compress knowledge from their training data through next-token conditional distributions. This limits tractable querying of this knowledge to start-to-end autoregressive sampling. However, many…
Runtime resource management for many-core systems is increasingly complex. The complexity can be due to diverse workload characteristics with conflicting demands, or limited shared resources such as memory bandwidth and power. Resource…
This work provides a novel convergence analysis for stochastic optimization in terms of stopping times, addressing the practical reality that algorithms are often terminated adaptively based on observed progress. Unlike prior approaches,…
This paper considers the task of learning users' preferences on a combinatorial set of alternatives, as generally used by online configurators, for example. In many settings, only a set of selected alternatives during past interactions is…
Static resource analysis determines the resource consumption (e.g., time complexity) of a program without executing it. Among the numerous existing approaches for resource analysis, affine type systems have been one dominant approach.…
We study the problem of policy optimization (PO) with linear temporal logic (LTL) constraints. The language of LTL allows flexible description of tasks that may be unnatural to encode as a scalar cost function. We consider LTL-constrained…
We propose a new (theoretical) computational model for the study of massive data processing with limited computational resources. Our model measures the complexity of reading the very large data sets in terms of the data size N and analyzes…
This article is concerned with automated complexity analysis of term rewrite systems. Since these systems underlie much of declarative programming, time complexity of functions defined by rewrite systems is of particular interest. Among…
We propose an amortized analysis that approximates the resource usage of a Haskell expression. Using the plugin API of GHC, we convert the Haskell code into a simplified representation called GHC Core. We then apply a type-based system…
This paper presents a class of Dynamic Multi-Armed Bandit problems where the reward can be modeled as the noisy output of a time varying linear stochastic dynamic system that satisfies some boundedness constraints. The class allows many…
This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional…
The quality of enumeration algorithms is often measured by their delay, that is, the maximal time spent between the output of two distinct solutions. If the goal is to enumerate $t$ distinct solutions for any given $t$, then another…
A simple lattice gas model with random fields and gravity is introduced to describe a system of grains moving in a disordered environment. Off equilibrium relaxations of bulk density and its two time correlation functions are numerically…
Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are…
Amortised analysis is a technique for proving a combined time bound for a batch of operations on a data structure, even if some of those operations are expensive. But the traditional method of amortised analysis yields incorrect time bounds…
Automata expressiveness is an essential feature in understanding which of the formalisms available should be chosen for modelling a particular problem. Probabilistic and stochastic automata are suitable for modelling systems exhibiting…