相关论文: On the Quantum Query Complexity of Detecting Trian…

The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponential random graph model) and in important…

This paper studies the round complexity of computing the weighted diameter and radius of a graph in the quantum CONGEST model. We present a quantum algorithm that $(1+o(1))$-approximates the diameter and radius with round complexity…

We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list,…

In this paper we present improved results on the problem of counting triangles in edge streamed graphs. For graphs with $m$ edges and at least $T$ triangles, we show that an extra look over the stream yields a two-pass treaming algorithm…

We present simple deterministic algorithms for subgraph finding and enumeration in the broadcast CONGEST model of distributed computation: -- For any constant $k$, detecting $k$-paths and trees on $k$ nodes can be done in $O(1)$ rounds. --…

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…

In this note we study the number of quantum queries required to identify an unknown multilinear polynomial of degree d in n variables over a finite field F_q. Any bounded-error classical algorithm for this task requires Omega(n^d) queries…

Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational…

We first prove a one-to-one correspondence between finding Hamiltonian cycles in a cubic planar graphs and finding trees with specific properties in dual graphs. Using this information, we construct an exact algorithm for finding…

In this short note, we give a novel algorithm for $O(1)$ round triangle counting in bounded arboricity graphs. Counting triangles in $O(1)$ rounds (exactly) is listed as one of the interesting remaining open problems in the recent survey of…

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…

The Local Search problem, which finds a local minimum of a black-box function on a given graph, is of both practical and theoretical importance to many areas in computer science and natural sciences. In this paper, we show that for the…

In this paper, we consider the parameterized quantum query complexity for graph problems. We design parameterized quantum query algorithms for $k$-vertex cover and $k$-matching problems, and present lower bounds on the parameterized quantum…

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 introduce a new approach and prove that the maximum number of triangles in a $C_5$-free graph on $n$ vertices is at most $$(1 + o(1)) \frac{1}{3 \sqrt 2} n^{3/2}.$$ We also show a connection to $r$-uniform hypergraphs without (Berge)…

Can Grover's algorithm speed up search of a physical region - for example a 2-D grid of size sqrt(n) by sqrt(n)? The problem is that sqrt(n) time seems to be needed for each query, just to move amplitude across the grid. Here we show that…

Lin and Lin have recently shown how starting with a classical query algorithm (decision tree) for a function, we may find upper bounds on its quantum query complexity. More precisely, they have shown that given a decision tree for a…

This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory…

Given an undirected, weighted graph, with $n$ vertices and $m$ edges, and two special vertices $s$ and $t$, the problem is to find the shortest path between them. We give two bounded-error quantum algorithms with improved runtime in the…

We present quantum algorithms for the following graph problems: finding a maximal bipartite matching in time O(n sqrt{m+n} log n), finding a maximal non-bipartite matching in time O(n^2 (sqrt{m/n} + log n) log n), and finding a maximal flow…