Algorithm Diniz
Formulation of the problem
Given a network, ie, directed graph in which each edge
is assigned
bandwidth
, and identified two peaks - the source and drain .
It locates in the network flow
from the source to the drain maximum.
A bit of histo

The minimum spanning tree. Prim's
algorithm
Dan weighted undirected graph with vertices and edges. We wanted to find a
subtree of the graph, which would connect all the vertices, and thus has the lowest
possible weight (ie, the sum of the weights of the e

Topological sorting
Dan directed graph with vertices and edges. Required to renumber the vertices
so that each rbro led from the top with a smaller number in the top with a big.
In other words, you want to find a permutation of vertices ( topological orde

The task assignment. The decision by a mincost-flow
The problem has two equivalent production:
Valued square matrix A [1.N, 1.N]. It is necessary to select N elements so
that each row and column has been selected exactly one element, and the sum of
these

The search algorithm of connected
components in a graph
Given an undirected graph with vertices and edges. Required to find in it all the
connected components, ie vertex split into groups such that within one group can be
reached from any one node to anot

Kuhn's algorithm for finding the greatest
matching in a bipartite graph
Given a bipartite graph comprising vertices and edges. Required to find the
maximum matching, ie, select the edges as much as possible, so that no one had
selected edge vertex in comm

The flow of minimum cost, minimum-cost
circulation. Algorithm removal cycles of
negative weight
Setting goals
Let - the network (network), that is a directed graph in which the vertices are
selected, the source and drain . The set of vertices is denoted b

The minimum spanning tree. Kruskal's
algorithm
Dan weighted undirected graph. We wanted to find a subtree of the graph, which
would connect all the vertices, and thus has the smallest weight (ie, the sum of the
weights of the edges) of all. This subtree i

The algorithm Floyd-Uorshella finding the
shortest paths between all pairs of vertices
Dan directed or undirected weighted graph with vertices. Required to find the
values of all variables
- length of the shortest path from vertex to vertex .
It is assume

Shortest path of fixed length, the number of
tracks fixed length
The following are solutions to these two problems, built on the same idea: the
reduction of the problem to the construction of the power matrix (with the usual
multiplication, and modified).

Search strongly connected component,
condensation build Count
Definitions, formulation of the problem
Dan directed graph whose set of vertices and edges of the set - . Loops and
multiple edges are allowed. We denote the number of vertices, through - the
n

Search Bridge Online
Given an undirected graph. A bridge is an edge whose removal makes the graph
disconnected (or, more precisely, increases the number of connected
components). It is required to find all the bridges in a given graph.
Informally, this pr

Search Bridges
Given an undirected graph. A bridge is an edge whose removal makes the graph
disconnected (or, more precisely, increases the number of connected
components). It is required to find all the bridges in a given graph.
Informally, this problem

Hungarian algorithm for solving the
assignment problem
Production Assignment Problem
The task assignment is placed quite naturally.
Here are a few options for setting (easy to see that they are all equivalent to each
other):
There are workers and jobs. Fo

Finding the minimal cut. Algorithm Curtains
Wagner
Formulation of the problem
Given an undirected weighted graph with vertices and edges. Slash called a
subset of vertices (actually cut - vertex partition into two sets: belonging and
everyone else). The w

Check the graph for bipartition and splitting
into two parts
Given an undirected graph. You want to check whether it is bipartite, ie whether it is
possible to divide it into two parts peaks so that no edges connecting two vertices of
one share. If the gr

Finding the most weight vertex-weighted
matchings
Given a bipartite graph G. For each vertex of the first part was not her
weight. Required to find the maximum weight matching, ie with the largest sum of the
weights of saturated peaks.
Below we describe a

Leviticus algorithm finding the shortest
paths from a given vertex to all other
vertices
Given a graph with N vertices and M edges, each of which indicated its weight
L i . Also, given the starting vertex V 0 .Required to find the shortest path from verte

Search in width
Search in width (width in the bypass, breadth-first search) - is one of the basic
algorithms on graphs.
As a result of search in width is the shortest path length in unweighted graph, ie, the
path that contains the smallest number of edges