Related papers: A Framework for Distributed Quantum Queries in the…
We show that, for every $k\geq 2$, $C_{2k}$-freeness can be decided in $O(n^{1-1/k})$ rounds in the \CONGEST{} model by a randomized Monte-Carlo distributed algorithm with one-sided error probability $1/3$. This matches the best…
In this paper we study the time complexity of the single-source reachability problem and the single-source shortest path problem for directed unweighted graphs in the Broadcast CONGEST model. We focus on the case where the diameter $D$ of…
Quantum computing as a promising technology can utilize stochastic solutions instead of deterministic approaches for complicated scenarios for which classical computing is inefficient, provided that both the concerns of the error-prone…
We introduce a structured quantum search algorithm that leverages entanglement maps and a fixed-point method to minimize oracle query complexity in unsorted datasets. By partitioning qubits into rows based on their entanglement order, the…
In the distributed triangle detection problem, we have an $n$-vertex network $G=(V,E)$ with one player for each vertex of the graph who sees the edges incident on the vertex. The players communicate in synchronous rounds using the edges of…
We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a…
In distributed networks, it is often useful for the nodes to be aware of dense subgraphs, e.g., such a dense subgraph could reveal dense subtructures in otherwise sparse graphs (e.g. the World Wide Web or social networks); these might…
We present a stack model for breaking down the complexity of entanglement-based quantum networks. More specifically, we focus on the structures and architectures of quantum networks and not on concrete physical implementations of network…
In this thesis, we present fast deterministic algorithm to find small cuts in distributed networks. Finding small min-cuts for a network is essential for ensuring the quality of service and reliability. Throughout this thesis, we use the…
Network decomposition is a central tool in distributed graph algorithms. We present two improvements on the state of the art for network decomposition, which thus lead to improvements in the (deterministic and randomized) complexity of…
Quantum networks are complex systems formed by the interaction among quantum processors through quantum channels. Analogous to classical computer networks, quantum networks allow for the distribution of quantum computation among quantum…
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…
In the quantum database search problem we are required to search for an item in a database. In this paper, we consider a generalization of this problem, where we are provided d identical copes of a database each with N items which we can…
The edge list model is arguably the simplest input model for graphs, where the graph is specified by a list of its edges. In this model, we study the quantum query complexity of three variants of the triangle finding problem. The first asks…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
Quantum computers connected through classical and quantum communication channels can be combined to function as a single unit to run large quantum circuits that each device is unable to execute on their own. The distributed quantum…
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…
Let $S$ be a string of length $n$ over an alphabet $\Sigma$ and let $Q$ be a subset of $\Sigma$ of size $q \geq 2$. The 'co-occurrence problem' is to construct a compact data structure that supports the following query: given an integer $w$…
Round complexity is an extensively studied metric of distributed algorithms. In contrast, our knowledge of the \emph{message complexity} of distributed computing problems and its relationship (if any) with round complexity is still quite…
In the LOCAL model, low-diameter decomposition is a useful tool in designing algorithms, as it allows us to shift from the general graph setting to the low-diameter graph setting, where brute-force information gathering can be done…