Related papers: Practical Trade-Offs for the Prefix-Sum Problem
We propose a special computational device which uses light rays for solving the subset-sum problem. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes.…
The A-hierarchy is a parametric analogue of the polynomial hierarchy in the context of paramterised complexity theory. We give a new characterisation of the A-hierarchy in terms of a generalisation of the SUBSET-SUM problem.
We consider formal verification of recursive programs with resource consumption. We introduce prefix replacement systems with non-negative integer counters which can be incremented and reset to zero as a formal model for such programs. In…
Given $(a_1, \dots, a_n, t) \in \mathbb{Z}_{\geq 0}^{n + 1}$, the Subset Sum problem ($\mathsf{SSUM}$) is to decide whether there exists $S \subseteq [n]$ such that $\sum_{i \in S} a_i = t$. There is a close variant of the $\mathsf{SSUM}$,…
The Subset Sum problem, which asks whether a set of $n$ integers has a subset summing to a target $t$, is a fundamental NP-complete problem in cryptography and combinatorial optimization. The classical meet-in-the-middle (MIM) algorithm of…
The binary indexed tree, or Fenwick tree, is a data structure that can efficiently update values and calculate prefix sums in an array. It allows both of these operations to be performed in $O(\log_2 N)$ time. Here we present a novel data…
In cloud computing, storage area networks, remote backup storage, and similar settings, stored data is modified with updates from new versions. Representing information and modifying the representation are both expensive. Therefore it is…
Language learning refers to the problem of inferring a mathematical model which accurately represents a formal language. Many language learning algorithms learn by asking certain types of queries about the language being modeled. Language…
We obtain a first non-trivial estimate for the sum of dilates problem in the case of groups of prime order, by showing that if $t$ is an integer different from $0, 1$ or -1 and if $\A \subset \Zp$ is not too large (with respect to $p$),…
In the 3SUM-Indexing problem the goal is to preprocess two lists of elements from $U$, $A=(a_1,a_2,\ldots,a_n)$ and $B=(b_1,b_2,...,b_n)$, such that given an element $c\in U$ one can quickly determine whether there exists a pair $(a,b)\in A…
In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets $X_m$ of the set $X_n$ (subset sum problem). Our algorithm has time complexity $T=O(C_{n}^{k})$ ($k=[m/2]$, which significantly…
This paper gives new explicit formulas for sums of powers of integers and their reciprocals.
The problem of Text Indexing is a fundamental algorithmic problem in which one wishes to preprocess a text in order to quickly locate pattern queries within the text. In the ever evolving world of dynamic and on-line data, there is also a…
We consider the Modular Subset Sum problem: given a multiset $X$ of integers from $\mathbb{Z}_m$ and a target integer $t$, decide if there exists a subset of $X$ with a sum equal to $t \pmod{m}$. Recent independent works by Cardinal and…
We introduce a new algorithm for constructing the generalized suffix array of a collection of highly similar strings. As a first step, we construct a compressed representation of the matching statistics of the collection with respect to a…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
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…
We discuss a problem of handling resource reservations. The resource can be reserved for some time, it can be freed or it can be queried what is the largest amount of reserved resource during a time interval. We show that the problem has a…
The $k$-subset sum problem over finite fields is a classical NP-complete problem.Motivated by coding theory applications, a more complex problem is the higher $m$-th moment $k$-subset sum problem over finite fields. We show that there is a…
In the Dictionary-based String Matching (DSM) problem, a retrieval system has access to a source sequence and stores the position of a certain number of strings in a posting table. When a user inquires the position of a string, the…