Drawing Clustered Graphs - School of Information Technologies

... Yworks wins a much larger market share, based on the competitive advantage of planarity-based methods, or Yworks finds that planarity-based methods are not useful, and drops the idea. ...

... Yworks wins a much larger market share, based on the competitive advantage of planarity-based methods, or Yworks finds that planarity-based methods are not useful, and drops the idea. ...

Quadratic Functions - Fundamental Coaching Centre

... table of values. In this project, you are required to find the minimum cost of extending the gas pipe. You may proceed as follows: Open a new spreadsheet, and type x in the cell A1 and C in the cell B1. Type 0 in the cell A2. Then type the formula = A2 + 0.05 into the cell A3 and fill down (using th ...

... table of values. In this project, you are required to find the minimum cost of extending the gas pipe. You may proceed as follows: Open a new spreadsheet, and type x in the cell A1 and C in the cell B1. Type 0 in the cell A2. Then type the formula = A2 + 0.05 into the cell A3 and fill down (using th ...

pptx - Electrical and Computer Engineering

... These slides are provided for the ECE 250 Algorithms and Data Structures course. The material in it reflects Douglas W. Harder’s best judgment in light of the information available to him at the time of preparation. Any reliance on these course slides by any party for any other purpose are the respo ...

... These slides are provided for the ECE 250 Algorithms and Data Structures course. The material in it reflects Douglas W. Harder’s best judgment in light of the information available to him at the time of preparation. Any reliance on these course slides by any party for any other purpose are the respo ...

High–performance graph algorithms from parallel sparse matrices

... structures and algorithms in our earlier work [5, 10]. The same principles apply to efficient operations on large sparse graphs. 1. Storage for a sparse matrix should be θ(max(n, nnz)) 2. An operation on sparse matrices should take time approximately proportional to the size of the data accessed and ...

... structures and algorithms in our earlier work [5, 10]. The same principles apply to efficient operations on large sparse graphs. 1. Storage for a sparse matrix should be θ(max(n, nnz)) 2. An operation on sparse matrices should take time approximately proportional to the size of the data accessed and ...

Efficient Algorithms and Problem Complexity

... Try to find algorithms running in time O(cn ) for a small c. Randomization Use algorithms that find the correct solution with high probability. Approximation Find a solution to an optimization problem not too far away from the optimum. Fixed-parameter algorithms Try to find algorithms that are effic ...

... Try to find algorithms running in time O(cn ) for a small c. Randomization Use algorithms that find the correct solution with high probability. Approximation Find a solution to an optimization problem not too far away from the optimum. Fixed-parameter algorithms Try to find algorithms that are effic ...

# Clique problem

In computer science, the clique problem refers to any of the problems related to finding particular complete subgraphs (""cliques"") in a graph, i.e., sets of elements where each pair of elements is connected.For example, the maximum clique problem arises in the following real-world setting. Consider a social network, where the graph’s vertices represent people, and the graph’s edges represent mutual acquaintance. To find a largest subset of people who all know each other, one can systematically inspect all subsets, a process that is too time-consuming to be practical for social networks comprising more than a few dozen people. Although this brute-force search can be improved by more efficient algorithms, all of these algorithms take exponential time to solve the problem. Therefore, much of the theory about the clique problem is devoted to identifying special types of graph that admit more efficient algorithms, or to establishing the computational difficulty of the general problem in various models of computation. Along with its applications in social networks, the clique problem also has many applications in bioinformatics and computational chemistry.Clique problems include: finding a maximum clique (largest clique by vertices),finding a maximum weight clique in a weighted graph,listing all maximal cliques (cliques that cannot be enlarged)solving the decision problem of testing whether a graph contains a clique larger than a given size.These problems are all hard: the clique decision problem is NP-complete (one of Karp's 21 NP-complete problems), the problem of finding the maximum clique is both fixed-parameter intractable and hard to approximate, and listing all maximal cliques may require exponential time as there exist graphs with exponentially many maximal cliques. Nevertheless, there are algorithms for these problems that run in exponential time or that handle certain more specialized input graphs in polynomial time.