Related papers: An Improved Combinatorial Algorithm for Boolean Ma…
Holographic search algorithms such as direct search and simulated annealing allow high-quality holograms to be generated at the expense of long execution times. This is due to single iteration computational costs of $O(N_x N_y)$ and number…
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…
We observe that any $T(n)$ time algorithm (quantum or classical) for several central linear algebraic problems, such as computing $\det(A)$, $tr(A^3)$, or $tr(A^{-1})$ for an $n \times n$ integer matrix $A$, yields a $O(T(n)) + \tilde…
While algebrisation constitutes a powerful technique in the design and analysis of centralised algorithms, to date there have been hardly any applications of algebraic techniques in the context of distributed graph algorithms. This work is…
We present two new quantum algorithms that either find a triangle (a copy of $K_{3}$) in an undirected graph $G$ on $n$ nodes, or reject if $G$ is triangle free. The first algorithm uses combinatorial ideas with Grover Search and makes…
We present approximation algorithms with O(n^3) processing time for the minimum vertex and edge guard problems in simple polygons. It is improved from previous O(n^4) time algorithms of Ghosh. For simple polygon, there are O(n^3) visibility…
We consider the problem of approximate counting of triangles and longer fixed length cycles in directed graphs. For triangles, T\v{e}tek [ICALP'22] gave an algorithm that returns a $(1 \pm \eps)$-approximation in…
Computing the diameter, and more generally, all eccentricities of an undirected graph is an important problem in algorithmic graph theory and the challenge is to identify graph classes for which their computation can be achieved in…
Until a few years ago, the fastest known matrix multiplication algorithm, due to Coppersmith and Winograd (1990), ran in time $O(n^{2.3755})$. Recently, a surge of activity by Stothers, Vassilevska-Williams, and Le Gall has led to an…
We present subquadratic algorithms in the algebraic decision-tree model for several \textsc{3Sum}-hard geometric problems, all of which can be reduced to the following question: Given two sets $A$, $B$, each consisting of $n$ pairwise…
The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…
In 1975, Valiant showed that Boolean matrix multiplication can be used for parsing context-free grammars (CFGs), yielding the asympotically fastest (although not practical) CFG parsing algorithm known. We prove a dual result: any CFG parser…
The clique problems, including $k$-CLIQUE and Triangle Finding, form an important class of computational problems; the former is an NP-complete problem, while the latter directly gives lower bounds for Matrix Multiplication. A number of…
We present an algorithm for finding a perfect matching in a $3$-edge-connected cubic graph that intersects every $3$-edge cut in exactly one edge. Specifically, we propose an algorithm with a time complexity of $O(n \log^4 n)$, which…
We demonstrate that a modification of the classical index calculus algorithm can be used to factor integers. More generally, we reduce the factoring problem to finding an overdetermined system of multiplicative relations in any factor base…
Consider a pair of plane straight-line graphs, whose edges are colored red and blue, respectively, and let n be the total complexity of both graphs. We present a O(n log n)-time O(n)-space technique to preprocess such pair of graphs, that…
Classic cache-oblivious parallel matrix multiplication algorithms achieve optimality either in time or space, but not both, which promotes lots of research on the best possible balance or tradeoff of such algorithms. We study modern…
Given a set of pairwise disjoint polygonal obstacles in the plane, finding an obstacle-avoiding Euclidean shortest path between two points is a classical problem in computational geometry and has been studied extensively. Previously,…
A constant-workspace algorithm has read-only access to an input array and may use only O(1) additional words of $O(\log n)$ bits, where $n$ is the size of the input. We assume that a simple $n$-gon is given by the ordered sequence of its…
We consider the problem of triangulating a polygon with $n$ vertices and $h$ holes, or relatedly the problem of computing the trapezoidal decomposition of a collection of $h$ disjoint simple polygonal chains with $n$ vertices total.…