Related papers: Solving Maximum Clique Problem for Protein Structu…
Molecular docking is a critical computational method in drug discovery used to predict the binding conformation and orientation of a ligand within a protein's binding site. Mapping this challenge onto a graph-based problem, specifically the…
We consider the problem of identifying a maximum clique in a given graph. We have proposed a mathematical model for this problem. The model resembles the matrix decomposition of the adjacency matrix of a given graph. The objective function…
Finding complete subgraphs in a graph, that is, cliques, is a key problem and has many real-world applications, e.g., finding communities in social networks, clustering gene expression data, modeling ecological niches in food webs, and…
DNA sequence alignment is important today as it is usually the first step in finding gene mutation, evolutionary similarities, protein structure, drug development and cancer treatment. Covid-19 is one recent example. There are many…
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, informatics, and many other areas. Although there exist several algorithms with acceptable runtimes for certain classes of…
The protein design problem involves finding polypeptide sequences folding into a given threedimensional structure. Its rigorous algorithmic solution is computationally demanding, involving a nested search in sequence and structure spaces.…
Fast, efficient and reliable algorithms for pairwise alignment of protein structures are in ever increasing demand for analyzing the rapidly growing data of protein structures. CLePAPS is a tool developed for this purpose. It distinguishes…
A variety of methods have been proposed for structure similarity calculation, which are called structure alignment or superposition. One major shortcoming in current structure alignment algorithms is in their inherent design, which is based…
The maximum labelled clique problem is a variant of the maximum clique problem where edges in the graph are given labels, and we are not allowed to use more than a certain number of distinct labels in a solution. We introduce a new…
Computational protein design aims at constructing novel or improved functions on the structure of a given protein backbone and has important applications in the pharmaceutical and biotechnical industry. The underlying combinatorial…
A matching cut is a partition of the vertex set of a graph into two sets $A$ and $B$ such that each vertex has at most one neighbor in the other side of the cut. The MATCHING CUT problem asks whether a graph has a matching cut, and has been…
Protein structural alignment is an important problem in computational biology. In this paper, we present first successes on provably optimal pairwise alignment of protein inter-residue distance matrices, using the popular Dali scoring…
The maximum vertex weight clique problem (MVWCP) is an important generalization of the maximum clique problem (MCP) that has a wide range of real-world applications. In situations where rigorous guarantees regarding the optimality of…
Circular permutation connects the N and C termini of a protein and concurrently cleaves elsewhere in the chain, providing an important mechanism for generating novel protein fold and functions. However, their in genomes is unknown because…
Finding the clique of maximum cardinality in an arbitrary graph is an NP-Hard problem that has many applications, which has motivated studies to solve it exactly despite its difficulty. The great majority of algorithms proposed in the…
A $k$-defective clique of an undirected graph $G$ is a subset of its vertices that induces a nearly complete graph with a maximum of $k$ missing edges. The maximum $k$-defective clique problem, which asks for the largest $k$-defective…
Protein representation learning is a challenging task that aims to capture the structure and function of proteins from their amino acid sequences. Previous methods largely ignored the fact that not all amino acids are equally important for…
We propose a minimal solution for the similarity registration (rigid pose and scale) between two sets of 3D lines, and also between a set of co-planar points and a set of 3D lines. The first problem is solved up to 8 discrete solutions with…
The maximum edge-weight clique problem is to find a clique whose sum of edge-weight is the maximum for a given edge-weighted undirected graph. The problem is NP-hard and some branch-and-bound algorithms have been proposed. In this paper, we…
We present CLIPPER+, an algorithm for finding maximal cliques in unweighted graphs for outlier-robust global registration. The registration problem can be formulated as a graph and solved by finding its maximum clique. This formulation…