Related papers: The root extraction problem for generic braids
Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the…
Many algorithms which exactly solve hard problems require branching on more or less complex structures in order to do their job. Those who design such algorithms often find themselves doing a meticulous analysis of numerous different cases…
This article provides a simple trigonometric method for determining how many roots of a quartic equation are real and how many are complex, without solving the equation. The approach replaces the quartic's classical discriminant -- a…
Given an arbitrary matrix $A\in\mathbb{R}^{n\times n}$, we consider the fundamental problem of computing $Ax$ for any $x\in\mathbb{R}^n$ such that $Ax$ is $s$-sparse. While fast algorithms exist for particular choices of $A$, such as the…
We study the time complexity of induced subgraph isomorphism problems where the pattern graph is fixed. The earliest known example of an improvement over trivial algorithms is by Itai and Rodeh (1978) who sped up triangle detection in…
In this paper we propose two new generic attacks on the Rank Syndrome Decoding (RSD) problem Let $C$ be a random $[n,k]$ rank code over $GF(q^m)$ and let $y=x+e$ be a received word such that $x \in C$ and the $Rank(e)=r$. The first attack…
We study the roots of a random polynomial over the field of p-adic numbers. For a random monic polynomial with coefficients in $\mathbb{Z}_p$, we obtain an asymptotic formula for the factorial moments of the number of roots of this…
Consider the problem of determining whether there exists a spanning hypertree in a given k-uniform hypergraph. This problem is trivially in P for k=2, and is NP-complete for k>= 4, whereas for k=3, there exists a polynomial-time algorithm…
The dispersion problem on graphs requires $k$ robots placed arbitrarily at the $n$ nodes of an anonymous graph, where $k \leq n$, to coordinate with each other to reach a final configuration in which each robot is at a distinct node of the…
$H$-Packing is the problem of finding a maximum number of vertex-disjoint copies of $H$ in a given graph $G$. $H$-Partition is the special case of finding a set of vertex-disjoint copies that cover each vertex of $G$ exactly once. Our goal…
We consider online algorithms for the $k$-server problem on trees of size $n$. Chrobak and Larmore proposed a $k$-competitive algorithm for this problem that has the optimal competitive ratio. However, the existing implementations have…
The Rooted Maximum Leaf Outbranching problem consists in finding a spanning directed tree rooted at some prescribed vertex of a digraph with the maximum number of leaves. Its parameterized version asks if there exists such a tree with at…
In this paper methods for simultaneous finding all roots of generalized polynomials are developed. These methods are related to the case when the roots are multiple. They possess cubic rate of convergence and they are as labour-consuming as…
Given a graph $G=(V,E)$ with non-negative real edge lengths and an integer parameter $k$, the Min-Max k-Tree Cover problem seeks to find a set of at most $k$ subtrees of $G$, such that the union of the trees is the vertex set $V$. The…
The class of graph deletion problems has been extensively studied in theoretical computer science, particularly in the field of parameterized complexity. Recently, a new notion of graph deletion problems was introduced, called deletion to…
Most computational models of dependency syntax consist of distributions over spanning trees. However, the majority of dependency treebanks require that every valid dependency tree has a single edge coming out of the ROOT node, a constraint…
Let $k\ge 1$ be an integer, and let $P= (f_1(x), \ldots, f_k(x) )$ be $k$ admissible linear polynomials over the integers, or \textit{the pattern}. We present two algorithms that find all integers $x$ where $\max{ \{f_i(x) \} } \le n$ and…
Let C be some class of objects equipped with a set of simplifying moves. When we apply these to a given object M in C as long as possible, we get a root of M. Our main result is that under certain conditions the root of any object exists…
Suppose f is a real univariate polynomial of degree D with exactly 4 monomial terms. We present an algorithm, with complexity polynomial in log D on average (relative to the stable log-uniform measure), for counting the number of real roots…
Following a recent improvement of Cardinal et al. on the complexity of a linear decision tree for $k$-SUM, resulting in $O(n^3 \log^3{n})$ linear queries, we present a further improvement to $O(n^2 \log^2{n})$ such queries.