Related papers: Mastermind with a Linear Number of Queries

String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…

We show that on graphs with n vertices, the 2-dimensional Weisfeiler-Leman algorithm requires at most O(n^2/log(n)) iterations to reach stabilization. This in particular shows that the previously best, trivial upper bound of O(n^2) is…

Palindromes are strings that read the same forward and backward. Problems of computing palindromic structures in strings have been studied for many years with a motivation of their application to biology. The longest palindrome problem is…

The coloring problem (i.e., computing the chromatic number of a graph) can be solved in $O^*(2^n)$ time, as shown by Bj\"orklund, Husfeldt and Koivisto in 2009. For $k=3,4$, better algorithms are known for the $k$-coloring problem.…

Enumerating maximal $k$-biplexes (MBPs) of a bipartite graph has been used for applications such as fraud detection. Nevertheless, there usually exists an exponential number of MBPs, which brings up two issues when enumerating MBPs, namely…

We study the CHAIN communication problem introduced by Cormode et al. [ICALP 2019]. It is a generalization of the well-studied INDEX problem. For $k\geq 1$, in CHAIN$_{n,k}$, there are $k$ instances of INDEX, all with the same answer. They…

A k-queue layout is a special type of a linear layout, in which the linear order avoids (k+1)-rainbows, i.e., k+1 independent edges that pairwise form a nested pair. The optimization goal is to determine the queue number of a graph, i.e.,…

The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…

In the two-dimensional orthogonal colored range counting problem, we preprocess a set, $P$, of $n$ colored points on the plane, such that given an orthogonal query rectangle, the number of distinct colors of the points contained in this…

Suppose that the vertices of a graph $G$ are colored with two colors in an unknown way. The color that occurs on more than half of the vertices is called the majority color (if it exists), and any vertex of this color is called a majority…

Given $n$ intervals on a line $\ell$, we consider the problem of moving these intervals on $\ell$ such that no two intervals overlap and the maximum moving distance of the intervals is minimized. The difficulty for solving the problem lies…

We consider a classical k-center problem in trees. Let T be a tree of n vertices and every vertex has a nonnegative weight. The problem is to find k centers on the edges of T such that the maximum weighted distance from all vertices to…

We consider the problem of learning an unknown partition of an $n$ element universe using rank queries. Such queries take as input a subset of the universe and return the number of parts of the partition it intersects. We give a simple…

Cutwidth is one of the classic layout parameters for graphs. It measures how well one can order the vertices of a graph in a linear manner, so that the maximum number of edges between any prefix and its complement suffix is minimized. As…

We show that, for any graph optimization problem in which the feasible solutions can be expressed by a formula in monadic second-order logic describing sets of vertices or edges and in which the goal is to minimize the sum of the weights in…

The ExactlyN problem in the number-on-forehead (NOF) communication setting asks $k$ players, each of whom can see every input but their own, if the $k$ input numbers add up to $N$. Introduced by Chandra, Furst and Lipton in 1983, ExactlyN…

We study the maximization version of the fundamental graph coloring problem. Here the goal is to color the vertices of a k-colorable graph with k colors so that a maximum fraction of edges are properly colored (i.e. their endpoints receive…

In responding to a question on Math Stackexchange, the author formulated the problem of determining the number of strings of balls colored in most $n$ colors with a number $k$ of repeated colors. In this paper, we formulate the problem more…

A $k$-coloring of a tournament is a partition of its vertices into $k$ acyclic sets. Deciding if a tournament is 2-colorable is NP-hard. A natural problem, akin to that of coloring a 3-colorable graph with few colors, is to color a…

Let $\textbf{k} := (k_1,\ldots,k_s)$ be a sequence of natural numbers. For a graph $G$, let $F(G;\textbf{k})$ denote the number of colourings of the edges of $G$ with colours $1,\dots,s$ such that, for every $c \in \{1,\dots,s\}$, the edges…