A heuristic method for solving triangle packing problem

Given a set of triangles and a rectangle container, the triangle packing problem is to determine if these triangles can be placed into the container without overlapping. Triangle packing problem is a special case of polygon packing problem and also NP-hard, so it is unlikely that an efficient and exact algorithm can be developed to solve this problem. In this paper, a new concept of rigid placement is proposed, based on which a discrete solution space called rigid solution space is constructed. Each solution in the rigid solution space can be built by continuously applying legal rigid placements one by one until all the triangles are placed into the rectangle container without overlapping. The proposed Least-Destruction-First (LDF) strategy determines which rigid placement has the privilege to go into the rectangle container. Based on this, a heuristic algorithm is proposed to solve the problem. Combining Least-Destruction-First strategy with backtracking, the corresponding backtracking algorithm is proposed. Computa- tional results show that our proposed algorithms are efficient and robust. With slight modification, these techniques can be con- veniently used for solving polygon packing problem.

HAPE3D—a new constructive algorithm for the 3D irregular packing problem

We propose a new constructive algorithm, called HAPE3 D, which is a heuristic algorithm based on the principle of minimum total potential energy for the 3D irregular packing problem, involving packing a set of irregularly shaped polyhedrons into a box-shaped container with fixed width and length but unconstrained height. The objective is to allocate all the polyhedrons in the container, and thus minimize the waste or maximize profit. HAPE3 D can deal with arbitrarily shaped polyhedrons, which can be rotated around each coordinate axis at different angles. The most outstanding merit is that HAPE3 D does not need to calculate no-fit polyhedron(NFP), which is a huge obstacle for the 3D packing problem. HAPE3 D can also be hybridized with a meta-heuristic algorithm such as simulated annealing. Two groups of computational experiments demonstrate the good performance of HAPE3 D and prove that it can be hybridized quite well with a meta-heuristic algorithm to further improve the packing quality.

A pure quasi-human algorithm for solving the cuboid packing problem

We excavate the wisdom from an old Chinese proverb ＂gold corner, silver side and strawy void＂, and further improve it into ＂maximum value in diamond cave＂ for solving the NP-hard cuboid packing problem. We extract, integrate and formalize the idea by west modern mathematical tools, and propose a pure quasi-human algorithm. The performance of the algorithm is evaluated on two sets of public benchmarks. For 100 strongly heterogeneous difficult benchmarks, experiments show an average packing utilization of 87.31%, which surpasses current best record reported in the literature by 1.83%. For 47 difficult benchmarks without orientation constraint, experiments show an average volume utilization of 92.05%, which improves current best record reported in the literature by 1.05%.

Mechanical Assembly Packing Problem Using Joint Constraints

The three-dimensional packing problem is generally on how to pack a set of models into a given bounding box using the smallest packaging volume. It is known as an NP-hard problem. When discussing the packing problem in mechanical field, the space utilization of a mechanism is low due to the constraint of mechanical joints between different mechanical parts. Although such a situation can be improved by breaking the mechanism into components at every joint, it burdens the user when reassembling the mechanism and may also reduce the service life of mechanical parts. In this paper, we propose a novel mechanism packing algorithm that deliberately considers the DOFs （degrees of freedom） of mechanical joints. With this algorithm, we construct the solution space according to each joint. While building the search tree of the splitting scheme, we do not break the joint, but move the joint. Therefore, the algorithm proposed in this paper just requires the minimal number of splits to meet the goal of space utilization. Numerical examples show that the proposed method is convenient and efficient to pack three-dimensional models into a given bounding box with high space utilization.

Two Bandwidth Packing Algorithms for the Centralized Wireless Network and Their Average-case Analysis

This paper presents a detail analysis of two bandwidth packing algorithms, used for processing connection requests in the centralized wireless network. Each call comes with a specific bandwidth request. A request can be satisfied only if there is sufficient bandwidth available during resource scheduling and allocation. Unsatisfied requests were held in a queue. The metric of bandwidth utilization ratio was used to quantify the performance of our algorithms. By theoretical analysis, our algorithms can improve the average bandwidth usage ratio significantly, about 8%~10% without adding much computation complexity. Moreover, our algorithms outperform next fit with fragmentation (NFF) algorithm when the bandwidth resource is scarce. In this paper, the contributions follows: Introducing bandwidth packing problem into wireless network; Proposing two new bandwidth packing algorithms for wireless network where the complicate scheduling algorithms are prohibited; Studying the average performance of our algorithms mathematically, which agree well with the simulation results.

Modified Packing Algorithm for Dynamic Energy-Saving in Cloud Computing Servers

Since the raising of the cloud computing, the applications of web service have been extended rapidly. However, the data centers of cloud computing also cause the problem of power consumption and the resources usually have not been used effectively. Decreasing the power consumption and enhancing resource utilization become main issues in cloud computing environment. In this paper, we propose a method, called MBFDP （modified best fit decreasing packing）, to decrease power consumption and enhance resource utilization of cloud computing servers. From the results of experiments, the proposed solution can reduce power consumption effectively and enhance the utilization of resources of servers.

An Optimal Algorithm for Solving Collision Distance Between Convex Polygons in Plane

In this paper,we study the problem,of calculating the minimum collision distance between two planar convex polygons when one of them moves to another along a given direction.First,several novel concepts and properties are explored,then an optimal algorithm OPFIV with time complexity O(log(n+m))is developed and its correctness and optimization are proved rigorously.

A New Fast Edge Detection Algorithm Based on NAM-structured Plane Decomposition

The nonsymmetry and antipacking pattern representation model （NAM）, inspired by the concept of the packing problem, uses a set of subpatterns to represent an original pattern. The NAM is a promising method for image representation because of its ability to focus on the interesting subsets of an image. In this paper, we develop a new method for gray-scale image representation based on NAM, called NAM-structured plane decomposition （NAMPD）, in which each subpattern is associated with a rectangular region in the image. The luminance function of pixels in this region is approximated by an oblique plane model. Then, we propose a new and fast edge detection algorithm based on NAMPD. The theoretical analyses and experimental results presented in this paper show that the edge detection algorithm using NAMPD performs faster than the classical ones because it permits the execution of operations on subpatterns instead of pixels.