Related papers: Enhanced algorithms for Local Search

For a family of graphs $\cal F$, the canonical Weighted $\cal F$ Vertex Deletion problem is defined as follows: given an $n$-vertex undirected graph $G$ and a weight function $w: V(G)\rightarrow\mathbb{R}$, find a minimum weight subset…

A temporal graph $G$ is a sequence $(G_t)_{t \in I}$ of graphs on the same vertex set of size $n$. The \emph{temporal exploration problem} asks for the length of the shortest sequence of vertices that starts at a given vertex, visits every…

In this work, we resolve the query complexity of global minimum cut problem for a graph by designing a randomized algorithm for approximating the size of minimum cut in a graph, where the graph can be accessed through local queries like…

The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…

We show a simple generalization of the quantum walk algorithm for search in backtracking trees by Montanaro (ToC 2018) to the case where vertices can have different times of computation. If a vertex $v$ in the tree of depth $D$ is computed…

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…

For $0\leq \rho\leq 1$ and a coloured graph $G$, a vertex $v$ is $\rho$-happy if at least $\rho \mathrm{deg}(v)$ of its neighbours have the same colour as $v$. Soft happy colouring of a partially coloured graph $G$ is the problem of finding…

Many combinatorial optimization problems can be approximated within $(1 \pm \epsilon)$ factors in $\text{poly}(\log n, 1/\epsilon)$ rounds in the LOCAL model via network decompositions [Ghaffari, Kuhn, and Maus, STOC 2018]. These approaches…

We present deterministic algorithms for the Hidden Subgroup Problem. The first algorithm, for abelian groups, achieves the same asymptotic worst-case query complexity as the optimal randomized algorithm, namely O($\sqrt{ n}\,$), where $n$…

Recently, \citeauthor*{akbari2021locality}~(ICALP 2023) studied the locality of graph problems in distributed, sequential, dynamic, and online settings from a {unified} point of view. They designed a novel $O(\log n)$-locality deterministic…

We describe algorithms to efficiently compute minimum $(s,t)$-cuts and global minimum cuts of undirected surface-embedded graphs. Given an edge-weighted undirected graph $G$ with $n$ vertices embedded on an orientable surface of genus $g$,…

A set $D$ of vertices of a graph is a \emph{defensive alliance} if, for each element of $D$, the majority of its neighbours are in $D$. We consider the notion of local minimality in this paper. We are interested in finding a locally minimal…

The Minimum Dominating Set (MDS) problem is one of the most fundamental and challenging problems in distributed computing. While it is well-known that minimum dominating sets cannot be approximated locally on general graphs, over the last…

The expansion of a hypergraph, a natural extension of the notion of expansion in graphs, is defined as the minimum over all cuts in the hypergraph of the ratio of the number of the hyperedges cut to the size of the smaller side of the cut.…

Dominating set is a set of vertices of a graph such that all other vertices have a neighbour in the dominating set. We propose a new order-based randomised local search (RLS$_o$) algorithm to solve minimum dominating set problem in large…

We present the first local problem that shows a super-constant separation between the classical randomized LOCAL model of distributed computing and its quantum counterpart. By prior work, such a separation was known only for an artificial…

Let $G$ be an $n$-vertex graph with $m$ edges. When asked a subset $S$ of vertices, a cut query on $G$ returns the number of edges of $G$ that have exactly one endpoint in $S$. We show that there is a bounded-error quantum algorithm that…

Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…

In a recent work, Esmer et al. describe a simple method - Approximate Monotone Local Search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more…

We consider two combinatorial problems. The first we call "search with wildcards": given an unknown n-bit string x, and the ability to check whether any subset of the bits of x is equal to a provided query string, the goal is to output x.…