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Best match graphs (BMGs) are a class of colored digraphs that naturally appear in mathematical phylogenetics and can be approximated with the help of similarity measures between gene sequences, albeit not without errors. The corresponding…
We propose a new methodology to develop heuristic algorithms using tree decompositions. Traditionally, such algorithms construct an optimal solution of the given problem instance through a dynamic programming approach. We modify this…
Combinatorial optimization is widely applied in a number of areas nowadays. Unfortunately, many combinatorial optimization problems are NP-hard which usually means that they are unsolvable in practice. However, it is often unnecessary to…
The NP-complete mutual-visibility (MV) problem currently lacks empirical analysis on its practical behaviour despite theoretical studies. This paper addresses this gap by implementing and evaluating three distinct algorithms -- a direct…
Many academic disciplines - including information systems, computer science, and operations management - face scheduling problems as important decision making tasks. Since many scheduling problems are NP-hard in the strong sense, there is a…
This work addresses the uniform parallel machine scheduling problem within an optimistic bilevel optimization framework. The leader seeks to minimize the weighted number of tardy jobs, while the follower aims to minimize the total…
Minimizing the rank of a matrix subject to constraints is a challenging problem that arises in many applications in control theory, machine learning, and discrete geometry. This class of optimization problems, known as rank minimization, is…
Identifying a small molecule from its mass spectrum is the primary open problem in computational metabolomics. This is typically cast as information retrieval: an unknown spectrum is matched against spectra predicted computationally from a…
Much combinatorial optimisation problems constitute a non-polynomial (NP) hard optimisation problem, i.e., they can not be solved in polynomial time. One such problem is finding the shortest route between two nodes on a graph.…
This paper studies constructive heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree that uses edges that are as similar as possible. Given an undirected labeled connected graph (i.e.,…
Many algorithms for processing probabilistic networks are dependent on the topological properties of the problem's structure. Such algorithms (e.g., clustering, conditioning) are effective only if the problem has a sparse graph captured by…
Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…
Lack of data on which to perform experimentation is a recurring issue in many areas of research, particularly in machine learning. The inability of most automated data mining techniques to be generalized to all types of data is inherently…
Given a connected, undirected graph whose edges are labelled (or coloured), the minimum labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest number of distinct labels (or colours). In recent work, the…
Targeted color-dots with varying shapes and sizes in images are first exhaustively identified, and then their multiscale 2D geometric patterns are extracted for testing spatial uniformness in a progressive fashion. Based on color theory in…
Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently…
The Colored Bin Packing Problem (CBPP) is a generalization of the Bin Packing Problem (BPP). The CBPP consists of packing a set of items, each with a weight and a color, in bins of limited capacity, minimizing the number of used bins and…
The crossing resolution of a non-planar drawing of a graph is the value of the minimum angle formed by any pair of crossing edges. Recent experiments have shown that the larger the crossing resolution is, the easier it is to read and…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
The A* algorithm is commonly used to solve NP-hard combinatorial optimization problems. When provided with a completely informed heuristic function, A* solves many NP-hard minimum-cost path problems in time polynomial in the branching…