Related papers: Improved Quantum Algorithm for Triangle Finding vi…
We study the complexity of determining the edge connectivity of a simple graph with cut queries. We show that (i) there is a bounded-error randomized algorithm that computes edge connectivity with $O(n)$ cut queries, and (ii) there is a…
The maximal clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry,…
We study algorithms for solving three problems on strings. The first one is the Most Frequently String Search Problem. The problem is the following. Assume that we have a sequence of $n$ strings of length $k$. The problem is finding the…
This paper employs a powerful argument, called an algorithmic argument, to prove lower bounds of the quantum query complexity of a multiple-block ordered search problem in which, given a block number i, we are to find a location of a target…
More than 25 years ago Chazelle~\emph{et al.} (FOCS 1991) studied the following question: Is it possible to cut any set of $n$ lines in ${\Bbb R}^3$ into a subquadratic number of fragments such that the resulting fragments admit a depth…
Consider the following generalization of the classic binary search problem: A searcher is required to find a hidden target vertex $x$ in a graph $G$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$.…
Given an $n$-vertex $m$-edge graph $G$ with non negative edge-weights, the girth of $G$ is the weight of a shortest cycle in $G$. For any graph $G$ with polynomially bounded integer weights, we present a deterministic algorithm that…
We study the enumeration of answers to Unions of Conjunctive Queries (UCQs) with optimal time guarantees. More precisely, we wish to identify the queries that can be solved with linear preprocessing time and constant delay. Despite the…
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…
In the Densest k-Subgraph problem, given a graph G and a parameter k, one needs to find a subgraph of G induced on k vertices that contains the largest number of edges. There is a significant gap between the best known upper and lower…
In this paper, it is demonstrated that the DNA-based algorithm [Ho et al. 2005] for solving an instance of the clique problem to any a graph G = (V, E) with n vertices and p edges and its complementary graph G1 = (V, E1) with n vertices and…
Given a simple, unweighted, undirected graph $G=(V,E)$ with $|V|=n$ and $|E|=m$, and parameters $0 < \varepsilon, \delta <1$, along with \texttt{Degree}, \texttt{Neighbour}, \texttt{Edge} and \texttt{RandomEdge} query access to $G$, we…
We consider the following stochastic matching problem on both weighted and unweighted graphs: A graph $G(V, E)$ along with a parameter $p \in (0, 1)$ is given in the input. Each edge of $G$ is realized independently with probability $p$.…
It is known that the dual of the general adversary bound can be used to build quantum query algorithms with optimal complexity. Despite this result, not many quantum algorithms have been designed this way. This paper shows another example…
Studies on Quantum Computing have been developed since the 1980s, motivating researches on quantum algorithms better than any classical algorithm possible. An example of such algorithms is Grover's algorithm, capable of finding $k$ (marked)…
The problem of (approximately) counting the number of triangles in a graph is one of the basic problems in graph theory. In this paper we study the problem in the streaming model. We study the amount of memory required by a randomized…
Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm…
We present a new algorithm for approximating the number of triangles in a graph $G$ whose edges arrive as an arbitrary order stream. If $m$ is the number of edges in $G$, $T$ the number of triangles, $\Delta_E$ the maximum number of…
In the $k$-cut problem, we want to find the lowest-weight set of edges whose deletion breaks a given (multi)graph into $k$ connected components. Algorithms of Karger \& Stein can solve this in roughly $O(n^{2k})$ time. On the other hand,…
Graph Crossing Number is a fundamental problem with various applications. In this problem, the goal is to draw an input graph $G$ in the plane so as to minimize the number of crossings between the images of its edges. Despite extensive…