|
Multi-commodity Flow Problem
The multi-commodity flow problem is a network flow problem with multiple commodities (flow demands) between different source and sink nodes. Definition Given a flow network \,G(V,E), where edge (u,v) \in E has capacity \,c(u,v). There are \,k commodities K_1,K_2,\dots,K_k, defined by \,K_i=(s_i,t_i,d_i), where \,s_i and \,t_i is the source and sink of commodity \,i, and \,d_i is its demand. The variable \,f_i(u,v) defines the fraction of flow \,i along edge \,(u,v), where \,f_i(u,v) \in ,1/math> in case the flow can be split among multiple paths, and \,f_i(u,v) \in \ otherwise (i.e. "single path routing"). Find an assignment of all flow variables which satisfies the following four constraints: (1) Link capacity: The sum of all flows routed over a link does not exceed its capacity. :\forall (u,v)\in E:\,\sum_^ f_i(u,v)\cdot d_i \leq c(u,v) (2) Flow conservation on transit nodes: The amount of a flow entering an intermediate node u is the same that exits the node. :\forall i \in K: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Flow Problem
In combinatorial optimization, network flow problems are a class of computational problems in which the input is a flow network (a graph with numerical capacities on its edges), and the goal is to construct a flow, numerical values on each edge that respect the capacity constraints and that have incoming flow equal to outgoing flow at all vertices except for certain designated terminals. Specific types of network flow problems include: *The maximum flow problem, in which the goal is to maximize the total amount of flow out of the source terminals and into the sink terminals *The minimum-cost flow problem, in which the edges have costs as well as capacities and the goal is to achieve a given amount of flow (or a maximum flow) that has the minimum possible cost *The multi-commodity flow problem, in which one must construct multiple flows for different commodities whose total flow amounts together respect the capacities * Nowhere-zero flow, a type of flow studied in combinatorics in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flow Network
In graph theory, a flow network (also known as a transportation network) is a directed graph where each edge has a capacity and each edge receives a flow. The amount of flow on an edge cannot exceed the capacity of the edge. Often in operations research, a directed graph is called a network, the vertices are called nodes and the edges are called arcs. A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, unless it is a source, which has only outgoing flow, or sink, which has only incoming flow. A network can be used to model traffic in a computer network, circulation with demands, fluids in pipes, currents in an electrical circuit, or anything similar in which something travels through a network of nodes. Definition A network is a graph , where is a set of vertices and is a set of 's edges – a subset of – together with a non-negative function , called the capacity function. Without loss of generality, we may assume that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimum Cost Flow Problem
The minimum-cost flow problem (MCFP) is an optimization and decision problem to find the cheapest possible way of sending a certain amount of flow through a flow network. A typical application of this problem involves finding the best delivery route from a factory to a warehouse where the road network has some capacity and cost associated. The minimum cost flow problem is one of the most fundamental among all flow and circulation problems because most other such problems can be cast as a minimum cost flow problem and also that it can be solved efficiently using the network simplex algorithm. Definition A flow network is a directed graph G=(V,E) with a source vertex s \in V and a sink vertex t \in V, where each edge (u,v) \in E has capacity c(u,v) > 0, flow f(u,v) and cost a(u,v), with most minimum-cost flow algorithms supporting edges with negative costs. The cost of sending this flow along an edge (u,v) is f(u,v)\cdot a(u,v). The problem requires an amount of flow d to be sent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circulation Problem
The circulation problem and its variants are a generalisation of network flow problems, with the added constraint of a lower bound on edge flows, and with flow conservation also being required for the source and sink (i.e. there are no special nodes). In variants of the problem, there are multiple commodities flowing through the network, and a cost on the flow. Definition Given flow network G(V,E) with: :l(v,w), lower bound on flow from node v to node w, :u(v,w), upper bound on flow from node v to node w, :c(v,w), cost of a unit of flow on (v,w) and the constraints: :l(v,w) \leq f(v,w) \leq u(v,w), :\sum_ f(u,w) = 0 (flow cannot appear or disappear in nodes). Finding a flow assignment satisfying the constraints gives a solution to the given circulation problem. In the minimum cost variant of the problem, minimize : \sum_ c(v,w) \cdot f(v,w). Multi-commodity circulation In a multi-commodity circulation problem, you also need to keep track of the flow of the individual com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Routing And Wavelength Assignment
The routing and wavelength assignment (RWA) problem is an optical networking problem with the goal of maximizing the number of optical connections. Definition The general objective of the RWA problem is to maximize the number of established connections. Each connection request must be given a route and wavelength. The wavelength must be consistent for the entire path, unless the usage of wavelength converters is assumed. Two connections requests can share the same optical link, provided a different wavelength is used. The RWA problem can be formally defined in an integer linear program (ILP). The ILP formulation given here is taken from. Maximize: :C_0(\rho,q) = \sum_^ m_i subject to :m_i \geq 0, integer, i = 1, 2, ..., N_ :c_ \in , i = 1, 2, ..., P, j = 1, 2, ..., W :C^TB \leq l_ :m \leq 1_WC^TA :m_i \leq q_i\rho, i = 1, 2, ..., N_ N_ is the number of source-destination pairs, while m_i is the number of connections established for each source-destination pair. L is the num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical Burst Switching
Optical burst switching (OBS) is an optical networking technique that allows dynamic sub-wavelength switching of data. OBS is viewed as a compromise between the yet unfeasible full optical packet switching (OPS) and the mostly static optical circuit switching (OCS). It differs from these paradigms because OBS control information is sent separately in a reserved optical channel and in advance of the data payload. These control signals can then be processed electronically to allow the timely setup of an optical light path to transport the soon-to-arrive payload. This is known as delayed reservation. Purpose The purpose of optical burst switching (OBS) is to dynamically provision sub-wavelength granularity by optimally combining electronics and optics. OBS considers sets of packets with similar properties called bursts. Therefore, OBS granularity is finer than optical circuit switching (OCS). OBS provides more bandwidth flexibility than wavelength routing but requires faster switching a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SONET
Synchronous optical networking (SONET) and synchronous digital hierarchy (SDH) are standardized protocols that transfer multiple digital bit streams synchronously over optical fiber using lasers or highly coherent light from light-emitting diodes (LEDs). At low transmission rates data can also be transferred via an electrical interface. The method was developed to replace the plesiochronous digital hierarchy (PDH) system for transporting large amounts of telephone calls and data traffic over the same fiber without the problems of synchronization. SONET and SDH, which are essentially the same, were originally designed to transport circuit mode communications (e.g., DS1, DS3) from a variety of different sources, but they were primarily designed to support real-time, uncompressed, circuit-switched voice encoded in PCM format. The primary difficulty in doing this prior to SONET/SDH was that the synchronization sources of these various circuits were different. This meant that each ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Register Allocation
In compiler optimization, register allocation is the process of assigning local automatic variables and expression results to a limited number of processor registers. Register allocation can happen over a basic block (''local register allocation''), over a whole function/ procedure (''global register allocation''), or across function boundaries traversed via call-graph (''interprocedural register allocation''). When done per function/procedure the calling convention may require insertion of save/restore around each call-site. Context Principle {, class="wikitable floatright" , + Different number of scalar registers in the most common architectures , - ! Architecture ! scope="col" , 32 bits ! scope="col" , 64 bits , - ! scope="row" , ARM , 15 , 31 , - ! scope="row" , Intel x86 , 8 , 16 , - ! scope="row" , MIPS , 32 , 32 , - ! scope="row" , POWER/PowerPC , 32 , 32 , - ! scope="row" , RISC-V , 16/32 , 32 , - ! scope="row" , SP ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-complete
In computational complexity theory, a problem is NP-complete when: # it is a problem for which the correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions. # the problem can be used to simulate every other problem for which we can verify quickly that a solution is correct. In this sense, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. If we could find solutions of some NP-complete problem quickly, we could quickly find the solutions of every other problem to which a given solution can be easily verified. The name "NP-complete" is short for "nondeterministic polynomial-time complete". In this name, "nondeterministic" refers to nondeterministic Turing machines, a way of mathematically formalizing the idea of a brute-force search algorithm. Polynomial time refers to an amount of time that is considered "quick" for a de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strongly NP-complete
In computational complexity, strong NP-completeness is a property of computational problems that is a special case of NP-completeness. A general computational problem may have numerical parameters. For example, the input to the bin packing problem is a list of objects of specific sizes and a size for the bins that must contain the objects—these object sizes and bin size are numerical parameters. A problem is said to be strongly NP-complete (NP-complete in the strong sense), if it remains NP-complete even when all of its numerical parameters are bounded by a polynomial in the length of the input. A problem is said to be strongly NP-hard if a strongly NP-complete problem has a polynomial reduction to it; in combinatorial optimization, particularly, the phrase "strongly NP-hard" is reserved for problems that are not known to have a polynomial reduction to another strongly NP-complete problem. Normally numerical parameters to a problem are given in positional notation, so a problem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear function#As a polynomial function, linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the mathematical optimization, optimization of a linear objective function, subject to linear equality and linear inequality Constraint (mathematics), constraints. Its feasible region is a convex polytope, which is a set defined as the intersection (mathematics), intersection of finitely many Half-space (geometry), half spaces, each of which is defined by a linear inequality. Its objective function is a real number, real-valued affine function, affine (linear) function defined on this polyhedron. A linear programming algorithm finds a point in the polytope where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas H
Thomas may refer to: People * List of people with given name Thomas * Thomas (name) * Thomas (surname) * Saint Thomas (other) * Thomas Aquinas (1225–1274) Italian Dominican friar, philosopher, and Doctor of the Church * Thomas the Apostle * Thomas (bishop of the East Angles) (fl. 640s–650s), medieval Bishop of the East Angles * Thomas (Archdeacon of Barnstaple) (fl. 1203), Archdeacon of Barnstaple * Thomas, Count of Perche (1195–1217), Count of Perche * Thomas (bishop of Finland) (1248), first known Bishop of Finland * Thomas, Earl of Mar (1330–1377), 14th-century Earl, Aberdeen, Scotland Geography Places in the United States * Thomas, Illinois * Thomas, Indiana * Thomas, Oklahoma * Thomas, Oregon * Thomas, South Dakota * Thomas, Virginia * Thomas, Washington * Thomas, West Virginia * Thomas County (other) * Thomas Township (other) Elsewhere * Thomas Glacier (Greenland) Arts, entertainment, and media * ''Thomas'' (Burton novel) 1969 novel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
