相关论文: Computing Minimum Tile Sets to Self-Assemble Color…
In this paper, we study the structure of the set of tilings produced by any given tile-set. For better understanding this structure, we address the set of finite patterns that each tiling contains. This set of patterns can be analyzed in…
In a vertex-colored graph $G = (V, E)$, a subset $S \subseteq V$ is said to be consistent if every vertex has a nearest neighbor in $S$ with the same color. The problem of computing a minimum cardinality consistent subset of a graph is…
A set is said to tile the integers if and only if the integers can be written as a disjoint union of translates of that set. We consider the problem of finding necessary and sufficient conditions for a finite set to tile the integers. For…
Context: Detecting arrays are mathematical structures aimed at fault identification in combinatorial interaction testing. However, they cannot be directly applied to systems that have constraints among test parameters. Such constraints are…
In this paper, we prove that if a finite number of rectangles, every of which has at least one integer side, perfectly tile a big rectangle then there exists a strategy which reduces the number of these tiles (rectangles) without violating…
In the trace reconstruction problem, one seeks to reconstruct a binary string $s$ from a collection of traces, each of which is obtained by passing $s$ through a deletion channel. It is known that $\exp(\tilde O(n^{1/5}))$ traces suffice to…
We discuss the self-assembly system of triangular tiles instead of square tiles, in particular right triangular tiles and equilateral triangular tiles. We show that the triangular tile assembly system, either deterministic or…
Consider the Maximum Weight Independent Set problem for rectangles: given a family of weighted axis-parallel rectangles in the plane, find a maximum-weight subset of non-overlapping rectangles. The problem is notoriously hard both in the…
Given an initial family of sets, we may take unions, intersections and complements of the sets contained in this family in order to form a new collection of sets; our construction process is done recursively until we obtain the last family.…
We investigate the role of nondeterminism in Winfree's abstract Tile Assembly Model (aTAM), which was conceived to model artificial molecular self-assembling systems constructed from DNA. Of particular practical importance is to find tile…
Narrow sieves, representative sets and divide-and-color are three breakthrough color coding-related techniques, which led to the design of extremely fast parameterized algorithms. We present a novel family of strategies for applying…
We develop and deploy a set of constraints for the purpose of calculating minimal sizes of lottery designs. Specifically, we find the minimum number of tickets of size six which are needed to match at least two balls on any draw of size…
The Generalized Sliding-Tile Puzzle (GSTP), allowing many square tiles on a board to move in parallel while enforcing natural geometric collision constraints on the movement of neighboring tiles, provide a high-fidelity mathematical model…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI,…
We present an $(1+\varepsilon)$-approximation algorithm with quasi-polynomial running time for computing the maximum weight independent set of polygons out of a given set of polygons in the plane (specifically, the running time is $n^{O(…
Discrete tomography deals with reconstructing finite spatial objects from lower dimensional projections and has applications for example in timetable design. In this paper we consider the problem of reconstructing a tile packing from its…
Neural architecture search (NAS) aims to automate the search procedure of architecture instead of manual design. Even if recent NAS approaches finish the search within days, lengthy training is still required for a specific architecture…
We study a family of sorting match puzzles on grids, which we call permutation match puzzles. In this puzzle, each row and column of a $n \times n$ grid is labeled with an ordering constraint -- ascending (A) or descending (D) -- and the…
In many real-world applications, the Pareto Set (PS) of a continuous multiobjective optimization problem can be a piecewise continuous manifold. A decision maker may want to find a solution set that approximates a small part of the PS and…