Related papers: Set Membership with a Few Bit Probes
Binary, or one-bit, representations of data arise naturally in many applications, and are appealing in both hardware implementations and algorithm design. In this work, we study the problem of data classification from binary data and…
The aim of this paper is twofold. First, we study the number of partitions of a positive integer $m$ into at most $n$ parts in a given set $A$. We prove that such a number is bounded by the $n$-th Fibonacci number $F(n)$ for any $m$ and…
Several algorithms with an approximation guarantee of $O(\log n)$ are known for the Set Cover problem, where $n$ is the number of elements. We study a generalization of the Set Cover problem, called the Partition Set Cover problem. Here,…
Given two strings $S$ and $P$, the Episode Matching problem is to find the shortest substring of $S$ that contains $P$ as a subsequence. The best known upper bound for this problem is $\tilde O(nm)$ by Das et al. (1997) , where $n,m$ are…
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…
In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in polynomial time. Using…
Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study a more general setting, in which some pairs of objects are incomparable. This generalization is relevant…
We prove two new space lower bounds for the problem of implementing a large shared register using smaller physical shared registers. We focus on the case where both the implemented and physical registers are single-writer, which means they…
A cofactor representation of an ideal element, that is, a representation in terms of the generators, can be considered as a certificate for ideal membership. Such a representation is typically not unique, and some can be a lot more…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
The research described in this note aims at solving the constructive membership problem for the class of quasisimple classical groups. Our algorithms are developed in the black-box group model; that is, they do not require specific…
Given string $S[1..N]$ and integer $k$, the {\em suffix selection} problem is to determine the $k$th lexicographically smallest amongst the suffixes $S[i... N]$, $1 \leq i \leq N$. We study the suffix selection problem in the cache-aware…
The Set Packing problem is, given a collection of sets $\mathcal{S}$ over a ground set $\mathcal{U}$, to find a maximum collection of sets that are pairwise disjoint. The problem is among the most fundamental NP-hard optimization problems…
Over the last few years, researchers have put significant effort into understanding of the notion of proportional representation in committee election. In particular, recently they have proposed the notion of proportionality degree. We…
Let n be a positive integer, and let R be a finitely presented (but not necessarily finite dimensional) associative algebra over a computable field. We examine algorithmic tests for deciding (1) if every n-dimensional representation of R is…
The NP-hard Minimum Common String Partition problem asks whether two strings $x$ and $y$ can each be partitioned into at most $k$ substrings, called blocks, such that both partitions use exactly the same blocks in a different order. We…
We consider the Minimum Coverage Kernel problem: given a set $B$ of $d$-dimensional boxes, find a subset of $B$ of minimum size covering the same region as $B$. This problem is $\mathsf{NP}$-hard, but as for many $\mathsf{NP}$-hard problems…
A parameterised Boolean equation system (PBES) is a set of equations that defines sets as the least and/or greatest fixed-points that satisfy the equations. This system is regarded as a declarative program defining functions that take a…
Given a sequence $A$ of $n$ numbers and an integer (target) parameter $1\leq i\leq n$, the (exact) selection problem asks to find the $i$-th smallest element in $A$. An element is said to be $(i,j)$-mediocre if it is neither among the top…
A secure set $S$ in a graph is defined as a set of vertices such that for any $X\subseteq S$ the majority of vertices in the neighborhood of $X$ belongs to $S$. It is known that deciding whether a set $S$ is secure in a graph is…