Related papers: Computational Complexity of Jumping Block Puzzles
In distributed matrix multiplication, a common scenario is to assign each worker a fraction of the multiplication task, by partitioning the input matrices into smaller submatrices. In particular, by dividing two input matrices into…
The modern integrated circuit is one of the most complex products that has been engineered to-date. It continues to grow in complexity as the years progress. As a result, very large-scale integrated (VLSI) circuit design now involves…
We study a popular puzzle game known variously as Clickomania and Same Game. Basically, a rectangular grid of blocks is initially colored with some number of colors, and the player repeatedly removes a chosen connected monochromatic group…
In the Token Sliding problem we are given a graph $G$ and two independent sets $I_s$ and $I_t$ in $G$ of size $k \geq 1$. The goal is to decide whether there exists a sequence $\langle I_1, I_2, \ldots, I_\ell \rangle$ of independent sets…
Random constraint satisfaction problems play an important role in computer science and combinatorics. For example, they provide challenging benchmark instances for algorithms and they have been harnessed in probabilistic constructions of…
We consider several computational problems related to conjugacy between subshifts of finite type, restricted to $k$-block codes: verifying a proposed $k$-block conjugacy, deciding if two shifts admit a $k$-block conjugacy, and reducing the…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
Different variations of alliances in graphs have been introduced into the graph-theoretic literature about twenty years ago. More broadly speaking, they can be interpreted as groups that collaborate to achieve a common goal, for instance,…
In this note, we consider the problem of finding a step-by-step transformation between two longest increasing subsequences in a sequence, namely Longest Increasing Subsequence Reconfiguration. We give a polynomial-time algorithm for…
\textsc{Directed Token Sliding} asks, given a directed graph and two sets of pairwise nonadjacent vertices, whether one can reach from one set to the other by repeatedly applying a local operation that exchanges a vertex in the current set…
We study the phase diagram and the algorithmic hardness of the random `locked' constraint satisfaction problems, and compare them to the commonly studied 'non-locked' problems like satisfiability of boolean formulas or graph coloring. The…
Suppose that we are given two independent sets $I_0$ and $I_r$ of a graph such that $|I_0| = |I_r|$, and imagine that a token is placed on each vertex in $I_0$. The token jumping problem is to determine whether there exists a sequence of…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
Various forms of sorting problems have been studied over the years. Recently, two kinds of sorting puzzle apps are popularized. In these puzzles, we are given a set of bins filled with colored units, balls or water, and some empty bins.…
A configuration of $n$ unit-cube-shaped \textit{modules} (or \textit{robots}) is a lattice-aligned placement of the $n$ modules so that their union is face-connected. The reconfiguration problem aims at finding a sequence of moves that…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
Reconfiguration graphs provide a way to represent relationships among solutions to a problem, and have been studied in many contexts. We investigate the reconfiguration graphs corresponding to minimum PSD forcing sets and minimum skew…
Clustering is one of the fundamental tasks in data analytics and machine learning. In many situations, different clusterings of the same data set become relevant. For example, different algorithms for the same clustering task may return…
The concept of statistical complexity is studied to characterize the classical kicked top model which plays important role in the qbit systems and the chaotic properties of the entanglement. This allows us to understand this driven…
Analogy has been shown to be important in many key cognitive abilities, including learning, problem solving, creativity and language change. For cognitive models of analogy, the fundamental computational question is how its inherent…