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We study ROUND-UFP and ROUND-SAP, two generalizations of the classical BIN PACKING problem that correspond to the unsplittable flow problem on a path (UFP) and the storage allocation problem (SAP), respectively. We are given a path with…
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…
Visual data, such as an image or a sequence of video frames, is often naturally represented as a point set. In this paper, we consider the fundamental problem of finding a nearest set from a collection of sets, to a query set. This problem…
Understanding the behavior of numerical metaheuristic optimization algorithms is critical for advancing their development and application. Traditional visualization techniques, such as convergence plots, trajectory mapping, and fitness…
Jamming in hard-particle packings has been the subject of considerable interest in recent years. In a paper by Torquato and Stillinger [J. Phys. Chem. B, 105 (2001)], a classification scheme of jammed packings into hierarchical categories…
Multigraph matching is a recent variant of the graph matching problem. In this framework, the optimization procedure considers several graphs and enforces the consistency of the matches along the graphs. This constraint can be formalized as…
The set of 2-dimensional packing problems builds an important class of optimization problems and Strip Packing together with 2-dimensional Bin Packing and 2-dimensional Knapsack is one of the most famous of these problems. Given a set of…
For dealing with the equal sphere packing problem, we propose a serial symmetrical relocation algorithm, which is effective in terms of the quality of the numerical results. We have densely packed up to 200 equal spheres in spherical…
We give an asymptotic approximation scheme (APTAS) for the problem of packing a set of circles into a minimum number of unit square bins. To obtain rational solutions, we use augmented bins of height $1+\gamma$, for some arbitrarily small…
The Circle Packing Theorem states that every planar graph can be represented as the tangency graph of a family of internally-disjoint circles. A well-known generalization is the Primal-Dual Circle Packing Theorem for 3-connected planar…
The proportional fair resource allocation problem is a major problem studied in flow control of networks, operations research, and economic theory, where it has found numerous applications. This problem, defined as the constrained…
This study proposes a new constraint handling technique for assisting metaheuristic optimization algorithms to solve constrained optimization problems more effectively and efficiently. Given any two solutions of any constrained optimization…
We consider the problem of finding all enclosing rectangles of minimum area that can contain a given set of rectangles without overlap. Our rectangle packer chooses the x-coordinates of all the rectangles before any of the y-coordinates. We…
Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…
Consolidation of loose packages into transport units is a fundamental activity offered by logistics service-providers. Moving the transport units instead of loose packages is faster (with one movement only, multiple packages are loaded…
Circle packing is widely used in visualization due to its aesthetic appeal and simplicity, particularly in tasks where the spatial arrangement and relationships between data are of interest, such as understanding proximity relationships…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
This paper outlines the ideas behind developing a graph-based heuristic-driven routing algorithm designed for a particular instance of a goods transportation problem with a single good type. The proposed algorithm solves the optimization…
In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…
Collage and packing techniques are widely used to organize geometric shapes into cohesive visual representations, facilitating the representation of visual features holistically, as seen in image collages and word clouds. Traditional…