Related papers: Upper and Lower Bounds on the Space Complexity of …
In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…
The indexing algorithms for the high-dimensional nearest neighbor search (NNS) with the best worst-case guarantees are based on the randomized Locality Sensitive Hashing (LSH), and its derivatives. In practice, many heuristic approaches…
The lock-free, ordered, linked list is an important, standard example of a concurrent data structure. An obvious, practical drawback of textbook implementations is that failed compare-and-swap (CAS) operations lead to retraversal of the…
Multi-step manipulation tasks where robots interact with their environment and must apply process forces based on the perceived situation remain challenging to learn and prone to execution errors. Accurately simulating these tasks is also…
In principle, higher-order networks that have multiple edge types are more informative than their lower-order counterparts. In practice, however, excessively rich information may be algorithmically infeasible to extract. It requires an…
This chapter is interested in the epistemology of algorithms. As I intend to approach the topic, this is an issue about epistemic justification. Current approaches to justification emphasize the transparency of algorithms, which entails…
We present a tight RMR complexity lower bound for the recoverable mutual exclusion (RME) problem, defined by Golab and Ramaraju \cite{GR2019a}. In particular, we show that any $n$-process RME algorithm using only atomic read, write,…
We study the problem of detecting zeros of continuous functions that are known only up to an error bound, extending the earlier theoretical work with explicit algorithms and experiments with an implementation. More formally, the robustness…
This paper studies the robustness of observability of a linear time-invariant system under sensor failures from a computational perspective. To be precise, the problem of determining the minimum number of sensors whose removal can destroy…
We design two Recoverable Mutual Exclusion (RME) locks for the system-wide crash model. Our first algorithm requires only $O(1)$ space per process, and achieves $O(1)$ worst-case RMR complexity in the CC model. Our second algorithm enhances…
The hope of the quantum computing field is that quantum architectures are able to scale up and realize fault-tolerant quantum computing. Due to engineering challenges, such ''cheap'' error correction may be decades away. In the meantime, we…
This paper examines several measures of space complexity of variants of stack automata: non-erasing stack automata and checking stack automata. These measures capture the minimum stack size required to accept every word in the language of…
This report considers how to inject external candidate solutions into the CMA-ES algorithm. The injected solutions might stem from a gradient or a Newton step, a surrogate model optimizer or any other oracle or search mechanism. They can…
In the static retrieval problem, a data structure must answer retrieval queries mapping a set of $n$ keys in a universe $[U]$ to $v$-bit values. Information-theoretically, retrieval data structures can use as little as $nv$ bits of space.…
Many people search for foreground objects to use when editing images. While existing methods can retrieve candidates to aid in this, they are constrained to returning objects that belong to a pre-specified semantic class. We instead propose…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
The fundamental tension between availability and consistency shapes the design of distributed storage systems. Classical results capture extreme points of this trade-off: the CAP theorem shows that strong models like linearizability…
A binary trie is a sequential data structure for a dynamic set on the universe $\{0,\dots,u-1\}$ supporting Search with $O(1)$ worst-case step complexity, and Insert, Delete, and Predecessor operations with $O(\log u)$ worst-case step…
Large language models (LLMs) are increasingly explored for NP-hard combinatorial optimization problems, but most existing methods emphasize feasible-instance solution generation and do not explicitly address infeasibility detection. We…
Capacitated Vertex Cover is the hard-capacitated variant of Vertex Cover: given a graph, a capacity for every vertex, and an integer $k$, the task is to select at most $k$ vertices that cover all edges and assign each edge to one of its…