Fractional coloringFractional coloring is a topic in a young branch of graph theory known as fractional graph theory. It is a generalization of ordinary graph coloring. In a traditional graph coloring, each vertex in a graph is assigned some color, and adjacent vertices — those connected by edges — must be assigned different colors. In a fractional coloring however, a set of colors is assigned to each vertex of a graph. The requirement about adjacent vertices still holds, so if two vertices are joined by an edge, they must have no colors in common.
Edge coloringIn graph theory, a proper edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color. For example, the figure to the right shows an edge coloring of a graph by the colors red, blue, and green. Edge colorings are one of several different types of graph coloring. The edge-coloring problem asks whether it is possible to color the edges of a given graph using at most k different colors, for a given value of k, or with the fewest possible colors.
Program optimizationIn computer science, program optimization, code optimization, or software optimization, is the process of modifying a software system to make some aspect of it work more efficiently or use fewer resources. In general, a computer program may be optimized so that it executes more rapidly, or to make it capable of operating with less memory storage or other resources, or draw less power. Although the word "optimization" shares the same root as "optimal", it is rare for the process of optimization to produce a truly optimal system.
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Register allocationIn 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.
Combinatorial optimizationCombinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combinatorial optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously mentioned, exhaustive search is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead.
Graph homomorphismIn the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a function between the vertex sets of two graphs that maps adjacent vertices to adjacent vertices. Homomorphisms generalize various notions of graph colorings and allow the expression of an important class of constraint satisfaction problems, such as certain scheduling or frequency assignment problems.
Optimizing compilerIn computing, an optimizing compiler is a compiler that tries to minimize or maximize some attributes of an executable computer program. Common requirements are to minimize a program's execution time, memory footprint, storage size, and power consumption (the last three being popular for portable computers). Compiler optimization is generally implemented using a sequence of optimizing transformations, algorithms which take a program and transform it to produce a semantically equivalent output program that uses fewer resources or executes faster.
Stack machineIn computer science, computer engineering and programming language implementations, a stack machine is a computer processor or a virtual machine in which the primary interaction is moving short-lived temporary values to and from a push down stack. In the case of a hardware processor, a hardware stack is used. The use of a stack significantly reduces the required number of processor registers. Stack machines extend push-down automata with additional load/store operations or multiple stacks and hence are Turing-complete.
Convex optimizationConvex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Call stackIn computer science, a call stack is a stack data structure that stores information about the active subroutines of a computer program. This kind of stack is also known as an execution stack, program stack, control stack, run-time stack, or machine stack, and is often shortened to just "the stack". Although maintenance of the call stack is important for the proper functioning of most software, the details are normally hidden and automatic in high-level programming languages.
Peephole optimizationPeephole optimization is an optimization technique performed on a small set of compiler-generated instructions; the small set is known as the peephole or window. Peephole optimization involves changing the small set of instructions to an equivalent set that has better performance.
Trampoline (computing)In computer programming, the word trampoline has a number of meanings, and is generally associated with jump instructions (i.e. moving to different code paths). Trampolines (sometimes referred to as indirect jump vectors) are memory locations holding addresses pointing to interrupt service routines, I/O routines, etc. Execution jumps into the trampoline and then immediately jumps out, or bounces, hence the term trampoline.
Processor registerA processor register is a quickly accessible location available to a computer's processor. Registers usually consist of a small amount of fast storage, although some registers have specific hardware functions, and may be read-only or write-only. In computer architecture, registers are typically addressed by mechanisms other than main memory, but may in some cases be assigned a memory address e.g. DEC PDP-10, ICT 1900.
Memory managementMemory management is a form of resource management applied to computer memory. The essential requirement of memory management is to provide ways to dynamically allocate portions of memory to programs at their request, and free it for reuse when no longer needed. This is critical to any advanced computer system where more than a single process might be underway at any time. Several methods have been devised that increase the effectiveness of memory management.
Register windowIn computer engineering, register windows are a feature which dedicates registers to a subroutine by dynamically aliasing a subset of internal registers to fixed, programmer-visible registers. Register windows are implemented to improve the performance of a processor by reducing the number of stack operations required for function calls and returns. One of the most influential features of the Berkeley RISC design, they were later implemented in instruction set architectures such as AMD Am29000, Intel i960, Sun Microsystems SPARC, and Intel Itanium.
Oil spillAn oil spill is the release of a liquid petroleum hydrocarbon into the environment, especially the marine ecosystem, due to human activity, and is a form of pollution. The term is usually given to marine oil spills, where oil is released into the ocean or coastal waters, but spills may also occur on land. Oil spills may be due to releases of crude oil from tankers, offshore platforms, drilling rigs and wells, as well as spills of refined petroleum products (such as gasoline and diesel fuel) and their by-products, heavier fuels used by large ships such as bunker fuel, or the spill of any oily refuse or waste oil.
Stack (abstract data type)In computer science, a stack is an abstract data type that serves as a collection of elements, with two main operations: Push, which adds an element to the collection, and Pop, which removes the most recently added element that was not yet removed. Additionally, a peek operation can, without modifying the stack, return the value of the last element added. Calling this structure a stack is by analogy to a set of physical items stacked one atop another, such as a stack of plates.
Instruction schedulingIn computer science, instruction scheduling is a compiler optimization used to improve instruction-level parallelism, which improves performance on machines with instruction pipelines. Put more simply, it tries to do the following without changing the meaning of the code: Avoid pipeline stalls by rearranging the order of instructions. Avoid illegal or semantically ambiguous operations (typically involving subtle instruction pipeline timing issues or non-interlocked resources).
Recursion (computer science)In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. Recursion solves such recursive problems by using functions that call themselves from within their own code. The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science. The power of recursion evidently lies in the possibility of defining an infinite set of objects by a finite statement.
