Related papers: Practical Trade-Offs for the Prefix-Sum Problem

3SUM-Indexing is a preprocessing variant of the 3SUM problem that has recently received a lot of attention. The best known time-space tradeoff for the problem is $T S^3 = n^{6}$ (up to logarithmic factors), where $n$ is the number of input…

We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…

PARITY is the problem of determining the parity of a string $f$ of $n$ bits given access to an oracle that responds to a query $x\in\{0,1,...,n-1\}$ with the $x^{\rm th}$ bit of the string, $f(x)$. Classically, $n$ queries are required to…

Subset sum is a very old and fundamental problem in theoretical computer science. In this problem, $n$ items with weights $w_1, w_2, w_3, \ldots, w_n$ are given as input and the goal is to find out if there is a subset of them whose weights…

The "Subset Sum problem" is a very well-known NP-complete problem. In this work, a top-k variation of the "Subset Sum problem" is considered. This problem has wide application in recommendation systems, where instead of k best objects the k…

This paper initializes the study of {\em range subgraph counting} and {\em range subgraph listing}, both of which are motivated by the significant demands in practice to perform graph analytics on subgraphs pertinent to only selected, as…

Given a set (or multiset) S of n numbers and a target number t, the subset sum problem is to decide if there is a subset of S that sums up to t. There are several methods for solving this problem, including exhaustive search,…

Prefix-tuning, or more generally continuous prompt tuning, has become an essential paradigm of parameter-efficient transfer learning. Using a large pre-trained language model (PLM), prefix-tuning can obtain strong performance by training…

Many applications of approximate membership query data structures, or filters, require only an incremental filter that supports insertions but not deletions. However, the design space of incremental filters is missing a "sweet spot" filter…

Given two strings $T$ and $S$ and a set of strings $P$, for each string $p \in P$, consider the unique substrings of $T$ that have $p$ as their prefix and $S$ as their suffix. Two problems then come to mind; the first problem being the…

Subset Sum is a classical optimization problem taught to undergraduates as an example of an NP-hard problem, which is amenable to dynamic programming, yielding polynomial running time if the input numbers are relatively small. Formally,…

The string-matching field has grown at a such complicated stage that various issues come into play when studying it: data structure and algorithmic design, database principles, compression techniques, architectural features, cache and…

A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…

Problems in additive number theory related to sum and difference sets, more general binary linear forms, and representation functions of additive bases for the integers and nonnegative integers.

In prefix coding over an infinite alphabet, methods that consider specific distributions generally consider those that decline more quickly than a power law (e.g., Golomb coding). Particular power-law distributions, however, model many…

Association rules is a very important part of data mining. It is used to find the interesting patterns from transaction databases. Apriori algorithm is one of the most classical algorithms of association rules, but it has the bottleneck in…

We address the problem of counting the number of strings in a collection where a given pattern appears, which has applications in information retrieval and data mining. Existing solutions are in a theoretical stage. We implement these…

We study the parameterized complexity of algorithmic problems whose input is an integer set $A$ in terms of the doubling constant $C := |A + A|/|A|$, a fundamental measure of additive structure. We present evidence that this new…

We propose a recursive algorithm for identifying all finite sequences of positive integers whose product equals their sum. Our method uses solutions of strictly shorter length that are iteratively extended in pursuit of a valid solution.…

Suffix trees are one of the most versatile data structures in stringology, with many applications in bioinformatics. Their main drawback is their size, which can be tens of times larger than the input sequence. Much effort has been put into…