相关论文: (Almost) tight bounds for randomized and quantum L…

We show that in the quantum query model the complexity of detecting a triangle in an undirected graph on $n$ nodes can be done using $O(n^{1+{3\over 7}}\log^{2}n)$ quantum queries. The same complexity bound applies for outputting the…

The current paper presents a new quantum algorithm for finding multicollisions, often denoted by $\ell$-collisions, where an $\ell$-collision for a function is a set of $\ell$ distinct inputs that are mapped by the function to the same…

Very recently, Khoury and Schild [FOCS 2025] showed that any randomized LOCAL algorithm that solves maximal matching requires $\Omega(\min\{\log \Delta, \log_\Delta n\})$ rounds, where $n$ is the number of nodes in the graph and $\Delta$ is…

Consider a graph problem that is locally checkable but not locally solvable: given a solution we can check that it is feasible by verifying all constant-radius neighborhoods, but to find a solution each node needs to explore the input graph…

In this work, we present a fast distributed algorithm for local potential problems: these are graph problems where the task is to find a locally optimal solution where no node can unilaterally improve the utility in its local neighborhood…

Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…

I improve the tight bound on quantum searching by Boyer et al. (quant-ph/9605034) to a matching bound, thus showing that for any probability of success Grovers quantum searching algorithm is optimal. E.g. for near certain success we have to…

We study randomized and quantum query (a.k.a. decision tree) complexity for all total Boolean functions, with emphasis to derandomization and dequantization (removing quantumness from algorithms). Firstly, we show that $D(f) = O(Q_1(f)^3)$…

An essential component of many sophisticated metaheuristics for solving combinatorial optimization problems is some variation of a local search routine that iteratively searches for a better solution within a chosen set of immediate…

In the typical model, a discrete-time coined quantum walk searching the 2D grid for a marked vertex achieves a success probability of $O(1/\log N)$ in $O(\sqrt{N \log N})$ steps, which with amplitude amplification yields an overall runtime…

This paper addresses the problem of finding the densest $k$-vertex subgraph in an arbitrary graph. This problem is NP-hard and has important applications in social network analysis, fraud detection, recommendation systems, and…

The goal of the ordered search problem is to find a particular item in an ordered list of n items. Using the adversary method, Hoyer, Neerbek, and Shi proved a quantum lower bound for this problem of (1/pi) ln n + Theta(1). Here, we find…

We study the problem of estimating the number of edges in an unknown graph. We consider a hybrid model in which an algorithm may issue independent set, degree, and neighbor queries. We show that this model admits strictly more efficient…

We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique…

In network analysis and graph mining, closeness centrality is a popular measure to infer the importance of a vertex. Computing closeness efficiently for individual vertices received considerable attention. The NP-hard problem of group…

We introduce a novel quantum algorithm for similar subgraph identification in form of an NP-hard cardinality-constrained binary quadratic optimization problem. Given a weighted reference graph with Laplacian $\boldsymbol{B}$, our algorithm…

Over the past decade, a long line of research has investigated the distributed complexity landscape of locally checkable labeling (LCL) problems on bounded-degree graphs, culminating in an almost-complete classification on general graphs…

In the paper, we investigated the influence of local and global interaction on the efficiency of continuous-time quantum spatial search. To do so, we analyzed numerically chimera graph, which is defined as 2D grid with each node replaced by…

This work studies the quantum query complexity of Boolean functions in a scenario where it is only required that the query algorithm succeeds with a probability strictly greater than 1/2. We show that, just as in the communication…

The problem of learning or reconstructing an unknown graph from a known family via partial-information queries arises as a mathematical model in various contexts. The most basic type of access to the graph is via \emph{edge queries}, where…