Related papers: 2-FREE-FLOOD-IT is polynomial
We consider problems related to the combinatorial game (Free-)Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations. We show that the minimum number of moves required…
The flooding games, which are called Flood-It, Mad Virus, or HoneyBee, are a kind of coloring games and they have been becoming popular online. In these games, each player colors one specified cell in his/her turn, and all connected…
Fixed-Flood-It and Free-Flood-It are combinatorial problems on graphs that generalize a very popular puzzle called Flood-It. Both problems consist of recoloring moves whose goal is to produce a monochromatic ("flooded") graph as quickly as…
We consider the complexity of problems related to the combinatorial game Free-Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations. Although computing the minimum…
We consider the complexity of problems related to the combinatorial game Free-Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations. Our main result is that computing…
The flood polynomial of a simple finite graph is a weight generating function that counts all flooding cascade sets of the graph. The flood polynomial is inspired by the water mechanics in the video game Minecraft. We give necessary…
The problem of determining the number of "flooding operations" required to make a given coloured graph monochromatic in the one-player combinatorial game Flood-It has been studied extensively from an algorithmic point of view, but basic…
We study the complexity of the popular one player combinatorial game known as Flood-It. In this game the player is given an n by n board of tiles where each tile is allocated one of c colours. The goal is to make the colours of all tiles…
Inspired by the eponymous hobby, we introduce Miniature Painting as the computational problem to paint a given graph $G=(V,E)$ according to a prescribed template $t \colon V \rightarrow C$, which assigns colors $C$ to the vertices of $G$.…
Solitaire {\sc Flood-it}, or {\sc Honey-Bee}, is a game played on a colored graph. The player resides in a source vertex. Originally his territory is the maximal connected, monochromatic subgraph that contains the source. A move consists of…
Multiplayer games on graphs are at the heart of theoretical descriptions of key evolutionary processes that govern vital social and natural systems. However, a comprehensive theoretical framework for solving multiplayer games with an…
We consider random labelings of finite graphs conditioned on a small fixed number of peaks. We introduce a continuum framework where a combinatorial graph is associated with a metric graph and edges are identified with intervals. Next we…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
In the recent years, several polynomial algorithms of a dynamical nature have been proposed to address the graph isomorphism problem. In this paper we propose a generalization of an approach exposed in cond-mat/0209112 and find that this…
In this paper, a new routing algorithm based on a flooding method is introduced. Flooding techniques have been used previously, e.g. for broadcasting the routing table in the ARPAnet [1] and other special purpose networks [3][4][5].…
A learned multi-dimensional index is a data structure that efficiently answers multi-dimensional orthogonal queries by understanding the data distribution using machine learning models. One of the existing problems is that the search…
The two-point correlation function of a Potts model on a graph $G$ may be expressed in terms of the flow polynomials of `Poissonian' random graphs derived from $G$ by replacing each edge by a Poisson-distributed number of copies of itself.…
We present a wavelet-based adaptive method for computing 3D multiscale flows in complex, time-dependent geometries, implemented on massively parallel computers. While our focus is on simulations of flapping insects, it can be used for other…
In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…
We study diffusion of colloids on a fluid-fluid interface using particle simulations and fluctuating hydrodynamics. Diffusion on a two-dimensional interface with three-dimensional hydrodynamics is known to be anomalous, with the collective…