Linear programming relaxationIn mathematics, the relaxation of a (mixed) integer linear program is the problem that arises by removing the integrality constraint of each variable. For example, in a 0–1 integer program, all constraints are of the form The relaxation of the original integer program instead uses a collection of linear constraints The resulting relaxation is a linear program, hence the name.
Windows PhoneWindows Phone (WP) is a discontinued family of mobile operating systems developed by Microsoft for smartphones as the replacement successor to Windows Mobile and Zune. Windows Phone featured a new user interface derived from the Metro design language. Unlike Windows Mobile, it was primarily aimed at the consumer market rather than the enterprise market. It was first launched in October 2010 with Windows Phone 7.
Windows 7Windows 7 is a major release of the Windows NT operating system developed by Microsoft. It was released to manufacturing on July 22, 2009, and became generally available on October 22, 2009. It is the successor to Windows Vista, released nearly three years earlier. Windows 7's server counterpart, Windows Server 2008 R2, was released at the same time. Windows 7 remained an operating system for use on personal computers, including home and business desktops, laptops, tablet PCs and media center PCs, and itself was replaced in November 2012 by Windows 8, the name spanning more than three years of the product.
Shortest path problemIn graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length of the segment.
Windows 8Windows 8 is a major release of the Windows NT operating system developed by Microsoft. It was released to manufacturing on August 1, 2012, and was made available for download via MSDN and TechNet on August 15, 2012. Nearly three months after its initial release, Windows 8 finally made its first retail appearance on October 26, 2012. Windows 8 is the first version of Microsoft Windows with a combination of 2D and 3D effects.
Windows 11Windows 11 is the latest major release of Microsoft's Windows NT operating system, released on October 5, 2021. It was a free upgrade to its predecessor, Windows 10 (2015), and is available for any Windows 10 devices that meet the new Windows 11 system requirements, but can also be installed on unsupported devices by bypassing the restrictions of system requirements.
Windows 2000Windows 2000 is a major release of the Windows NT operating system developed by Microsoft and designed for businesses. It was the direct successor to Windows NT 4.0, and was released to manufacturing on December 15, 1999, and was officially released to retail on February 17, 2000 and September 26, 2000 for Windows 2000 Datacenter Server. It was Microsoft's business operating system until the introduction of Windows XP Professional in 2001. Windows 2000 introduced NTFS 3.0, , as well as basic and dynamic disk storage.
Cutting stock problemIn operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of stock material, such as paper rolls or sheet metal, into pieces of specified sizes while minimizing material wasted. It is an optimization problem in mathematics that arises from applications in industry. In terms of computational complexity, the problem is an NP-hard problem reducible to the knapsack problem. The problem can be formulated as an integer linear programming problem.
Arc routingArc routing problems (ARP) are a category of general routing problems (GRP), which also includes node routing problems (NRP). The objective in ARPs and NRPs is to traverse the edges and nodes of a graph, respectively. The objective of arc routing problems involves minimizing the total distance and time, which often involves minimizing deadheading time, the time it takes to reach a destination.
Hamiltonian path problemIn the mathematical field of graph theory the Hamiltonian path problem and the Hamiltonian cycle problem are problems of determining whether a Hamiltonian path (a path in an undirected or directed graph that visits each vertex exactly once) or a Hamiltonian cycle exists in a given graph (whether directed or undirected). Both problems are NP-complete.
