Related papers: Confluent Persistence Revisited

We describe two efficient on-line algorithms to simplify weighted graphs by eliminating degree-two vertices. Our algorithms are on-line in that they react to updates on the data, keeping the simplification up-to-date. The supported updates…

Deep learning often faces the challenge of efficiently processing dynamic inputs, such as sensor data or user inputs. For example, an AI writing assistant is required to update its suggestions in real time as a document is edited.…

Consistent hashing is a technique that can minimize key remapping when the number of hash buckets changes. The paper proposes a fast consistent hash algorithm (called power consistent hash) that has $O(1)$ expected time for key lookup,…

In this work, we explore links between natural homology and persistent homology for the classification of directed spaces. The former is an algebraic invariant of directed spaces, a semantic model of concurrent programs. The latter was…

The past decade has witnessed many interesting algorithms for maintaining statistics over a data stream. This paper initiates a theoretical study of algorithms for monitoring distributed data streams over a time-based sliding window (which…

Sorting is one of the most fundamental algorithms in computer science. Recently, Learned Sorts, which use machine learning to improve sorting speed, have attracted attention. While existing studies show that Learned Sort is empirically…

Token prediction stability remains a challenge in autoregressive generative models, where minor variations in early inference steps often lead to significant semantic drift over extended sequences. A structured modulation mechanism was…

We describe a new methodology for studying persistence of topological features across a family of spaces or point-cloud data sets, called zigzag persistence. Building on classical results about quiver representations, zigzag persistence…

We consider the classical problem of representing a collection of priority queues under the operations \Findmin{}, \Insert{}, \Decrease{}, \Meld{}, \Delete{}, and \Deletemin{}. In the comparison-based model, if the first four operations are…

We provide a data structure for maintaining an embedding of a graph on a surface (represented combinatorially by a permutation of edges around each vertex) and computing generators of the fundamental group of the surface, in amortized time…

In this work, we explore whether modeling recurrence into the Transformer architecture can both be beneficial and efficient, by building an extremely simple recurrent module into the Transformer. We compare our model to baselines following…

This paper shows the weighted matching problem on general graphs can be solved in time $O(n(m + n\log n))$ for $n$ and $m$ the number of vertices and edges, respectively. This was previously known only for bipartite graphs. The crux is a…

Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the…

We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…

For obtaining optimal first-order convergence guarantee for stochastic optimization, it is necessary to use a recurrent data sampling algorithm that samples every data point with sufficient frequency. Most commonly used data sampling…

We consider Online Convex Optimization (OCO) in the setting where the costs are $m$-strongly convex and the online learner pays a switching cost for changing decisions between rounds. We show that the recently proposed Online Balanced…

It is well-known that the cohomology ring has a richer structure than homology groups. However, until recently, the use of cohomology in persistence setting has been limited to speeding up of barcode computations. Some of the recently…

Price-based revenue management is an important problem in operations management with many practical applications. The problem considers a retailer who sells a product (or multiple products) over $T$ consecutive time periods and is subject…

Recent trends in information management involve the periodic transcription of data onto secondary devices in a networked environment, and the proper scheduling of these transcriptions is critical for efficient data management. To assist in…

Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…