相关论文: Computing Minimum Tile Sets to Self-Assemble Color…
In the abstract Tile Assembly Model (aTAM) square tiles self-assemble, autonomously binding via glues on their edges, to form structures. Algorithmic aTAM systems can be designed in which the patterns of tile attachments are forced to…
Given a graph $G$, and terminal vertices $s$ and $t$, the TRACKING PATHS problem asks to compute a minimum number of vertices to be marked as trackers, such that the sequence of trackers encountered in each s-t path is unique. TRACKING…
This project mathematically models the self-assembly of DNA nanostructures in the shape of select Archimedean graphs using the flexible tile model. Under three different sets of restrictions called scenarios, we employ principles of linear…
Self-assembly is a process found everywhere in the Nature. In particular, it is known that DNA self-assembly is Turing universal. Thus one can do arbitrary computations or build nano-structures using DNA self-assembly. In order to…
Self-synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization. Difference systems of sets are combinatorial designs which specify the…
We prove that some exact geometric pattern matching problems reduce in linear time to $k$-SUM when the pattern has a fixed size $k$. This holds in the real RAM model for searching for a similar copy of a set of $k\geq 3$ points within a set…
A forcing set $S$ in a combinatorial problem is a set of elements such that there is a unique solution that contains all the elements in $S$. An anti-forcing set is the symmetric concept: a set $S$ of elements is called an anti-forcing set…
Sorting networks are oblivious sorting algorithms with many practical applications and rich theoretical properties. Propositional encodings of sorting networks are a key tool for proving concrete bounds on the minimum number of comparators…
Algorithmic self-assembly, a generalization of crystal growth processes, has been proposed as a mechanism for autonomous DNA computation and for bottom-up fabrication of complex nanostructures. A `program' for growing a desired structure…
The computational complexity of tiling finite simply connected regions with a fixed set of tiles is studied in this paper. We show that the problem of tiling simply connected regions with a fixed set of $23$ Wang tiles is NP-complete. As a…
The process of self-assembly is guided by the minimization of free energy, which limits the symmetries available for assembly and ultimately the usefulness of devices fabricated in this fashion. Here, we demonstrate experimentally for the…
For generic maps from compact surfaces with boundary into the plane we develop an explicit algorithm for minimizing both the number of cusps and the number of components of the singular locus. More precisely, we minimize among maps with…
We are concerned with the problem of designing large families of subsets over a common labeled ground set that have small pairwise intersections and the property that the maximum discrepancy of the label values within each of the sets is…
We consider the parameterized complexity of the problem of tracking shortest s-t paths in graphs, motivated by applications in security and wireless networks. Given an undirected and unweighted graph with a source s and a destination t,…
The chromatic sum of a graph is the smallest sum of colors among all proper colorings with natural numbers. The strength is the minimum number of colors needed to achieve the chromatic sum. We construct for each positive integer k a tree…
Color theme or color palette can deeply influence the quality and the feeling of a photograph or a graphical design. Although color palettes may come from different sources such as online crowd-sourcing, photographs and graphical designs,…
Let $G$ be a graph such that each vertex has its list of available colors, and assume that each list is a subset of the common set consisting of $k$ colors. For two given list colorings of $G$, we study the problem of transforming one into…
Many constraint satisfaction problems involve synthesizing subgraphs that satisfy certain reachability constraints. This paper presents programs in Picat for four problems selected from the recent LP/CP programming competitions. The…
The method for a problem solution of expenditures reduction of computing resources and time is developed at a pattern recognition, with the way of construction of the minimum tests sets or separate minimum tests on Boolean matrixes is…
Machine learning (ML) is ubiquitous in modern life. Since it is being deployed in technologies that affect our privacy and safety, it is often crucial to understand the reasoning behind its decisions, warranting the need for explainable AI.…