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Rummikub is a tile-based game in which each player starts with a hand of $14$ tiles. A tile has a value and a suit. The players form sets consisting of tiles with the same suit and consecutive values (runs) or tiles with the same value and different suits (groups). The corresponding optimization problem is, given a hand of tiles, to form valid sets such that the score (sum of tile values) is maximized. We first present an algorithm that solves this problem in polynomial time. Next, we analyze the impact on the computational complexity when we generalize over various input parameters. Finally, we attempt to better understand some aspects involved in human play by means of an experiment that considers counting problems related to the number of possible immediately winning hands.
The question if a given partial solution to a problem can be extended reasonably occurs in many algorithmic approaches for optimization problems. For instance, when enumerating minimal dominating sets of a graph $G=(V,E)$, one usually arrives at the
This paper is aimed to investigate some computational aspects of different isoperimetric problems on weighted trees. In this regard, we consider different connectivity parameters called {it minimum normalized cuts}/{it isoperimteric numbers} defined
We study the query complexity of quantum learning problems in which the oracles form a group $G$ of unitary matrices. In the simplest case, one wishes to identify the oracle, and we find a description of the optimal success probability of a $t$-query
Best match graphs (BMGs) are vertex-colored directed graphs that were introduced to model the relationships of genes (vertices) from different species (colors) given an underlying evolutionary tree that is assumed to be unknown. In real-life applicat
The even cycle problem for both undirected and directed graphs has been the topic of intense research in the last decade. In this paper, we study the computational complexity of emph{cycle length modularity problems}. Roughly speaking, in a cycle len