Related papers: An O(1) Solution to the Prefix Sum Problem on a Sp…
Subset-Sum and k-SAT are two of the most extensively studied problems in computer science, and conjectures about their hardness are among the cornerstones of fine-grained complexity. One of the most intriguing open problems in this area is…
The problem of exactly summing n floating-point numbers is a fundamental problem that has many applications in large-scale simulations and computational geometry. Unfortunately, due to the round-off error in standard floating-point…
Large Language Model (LLM) has exhibited strong reasoning ability in text-based contexts across various domains, yet the limitation of context window poses challenges for the model on long-range inference tasks and necessitates a memory…
We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: 1. Each comparison can be erroneous with some probability $1 - p$. 2. At each stage $k$ comparisons can be performed in parallel and a…
We consider a monotone submodular maximization problem whose constraint is described by a logic formula on a graph. Formally, we prove the following three `algorithmic metatheorems.' (1) If the constraint is specified by a monadic…
We describe an algorithm computing an optimal prefix free code for $n$ unsorted positive weights in time within $O(n(1+\lg \alpha))\subseteq O(n\lg n)$, where the alternation $\alpha\in[1..n-1]$ measures the amount of sorting required by…
We present a compressed representation of tries based on top tree compression [ICALP 2013] that works on a standard, comparison-based, pointer machine model of computation and supports efficient prefix search queries. Namely, we show how to…
We study the shared processor scheduling problem with a single shared processor where a unit time saving (weight) obtained by processing a job on the shared processor depends on the job. A polynomial-time optimization algorithm has been…
Given a set of $n$ input integers, the Equal Subset Sum problem asks us to find two distinct subsets with the same sum. In this paper we present an algorithm that runs in time $O^*(3^{0.387n})$ in the~average case, significantly improving…
We examine the complexity of the online Dictionary Matching with One Gap Problem (DMOG) which is the following. Preprocess a dictionary $D$ of $d$ patterns, where each pattern contains a special gap symbol that can match any string, so that…
This paper proposes an efficient and novel method to address range search on multidimensional points in $\theta(t)$ time, where $t$ is the number of points reported in $\Re^k$ space. This is accomplished by introducing a new data structure,…
Recent advances in optimization theory have shown that smooth strongly convex finite sums can be minimized faster than by treating them as a black box "batch" problem. In this work we introduce a new method in this class with a theoretical…
Sequence discriminative training is a great tool to improve the performance of an automatic speech recognition system. It does, however, necessitate a sum over all possible word sequences, which is intractable to compute in practice.…
Recent advances in spoken language technologies and the introduction of many customer facing products, have given rise to a wide customer reliance on smart personal assistants for many of their daily tasks. In this paper, we present a…
With direct access to human-written reference as memory, retrieval-augmented generation has achieved much progress in a wide range of text generation tasks. Since better memory would typically prompt better generation~(we define this as…
In this work, we tackle a natural variation of the String Matching Problem on the case of a dynamic pattern, that is, given a static text $T$ and a pattern $P$, we want to support character additions and deletions to the pattern, and after…
We deal with the problem of maintaining the suffix tree indexing structure for a fully-online collection of multiple strings, where a new character can be prepended to any string in the collection at any time. The only previously known…
We study the following substring suffix selection problem: given a substring of a string T of length n, compute its k-th lexicographically smallest suffix. This a natural generalization of the well-known question of computing the maximal…
We present a collection of new results on problems related to 3SUM, including: 1. The first truly subquadratic algorithm for $\ \ \ \ \ $ 1a. computing the (min,+) convolution for monotone increasing sequences with integer values bounded by…
Large language models (LLMs) acquire knowledge during pre-training, but over time, this knowledge may become incorrect or outdated, necessitating updates after training. Knowledge editing techniques address this issue without the need for…