A Message-Passing Algorithm for Counting Short Cycles in a Graph

A message-passing algorithm for counting short cycles in a graph is presented. For bipartite graphs, which are of particular interest in coding, the algorithm is capable of counting cycles of length g, g +2,..., 2g - 2, where g is the girth of the graph. For a general (non-bipartite) graph, cycles of length g; g + 1, ..., 2g - 1 can be counted. The algorithm is based on performing integer additions and subtractions in the nodes of the graph and passing extrinsic messages to adjacent nodes. The complexity of the proposed algorithm grows as $O(g|E|^2)$, where $|E|$ is the number of edges in the graph. For sparse graphs, the proposed algorithm significantly outperforms the existing algorithms in terms of computational complexity and memory requirements.Comment: Submitted to IEEE Trans. Inform. Theory, April 21, 2010

Distributed Optimization for Power Systems with Radial Partitioning

This paper proposes group-based distributed optimization algorithms on top of intelligent partitioning for the optimal power flow (OPF) problem. Radial partitioning of the graph of a network is introduced as a systematic way to split a large-scale problem into more tractable sub-problems, which can potentially be solved efficiently with methods such as convex relaxations. The simple implementation of a Distributed Consensus Algorithm (DiCA) with very few parameters makes it viable for different parameter selection methods, which are crucial for the fast convergence of the distributed algorithms. The DiCA algorithm returns more accurate solutions to the tested problems with fewer iterations than component-based algorithms. Our numerical results show the performance of the algorithms for different power network instances and the effect of parameter selection. A software package DiCARP is created, which is implemented in Python using the Pyomo optimization package.Comment: 7 pages, 4 figure

Minimum Cost Homomorphisms to Reflexive Digraphs

For digraphs $G$ and $H$, a homomorphism of $G$ to $H$ is a mapping $f:\ V(G)\dom V(H)$such that$uv\in A(G)$implies$f(u)f(v)\in A(H)$. If moreover each vertex$u \in V(G)$is associated with costs$c_i(u), i \in V(H)$, then the cost of a homomorphism$f$is$\sum_{u\in V(G)}c_{f(u)}(u)$. For each fixed digraph$H, the {\em minimum cost homomorphism problem} for H$, denoted MinHOM($H$), is the following problem. Given an input digraph$G$, together with costs$c_i(u)$,$u\in V(G)$,$i\in V(H)$, and an integer$k$, decide if$G$admits a homomorphism to$H$of cost not exceeding$k. We focus on the minimum cost homomorphism problem for {\em reflexive} digraphs H$(every vertex of$H$has a loop). It is known that the problem MinHOM($H$) is polynomial time solvable if the digraph$H has a {\em Min-Max ordering}, i.e., if its vertices can be linearly ordered by <$so that$i<j, s<r$and$ir, js \in A(H)$imply that$is \in A(H)$and$jr \in A(H)$. We give a forbidden induced subgraph characterization of reflexive digraphs with a Min-Max ordering; our characterization implies a polynomial time test for the existence of a Min-Max ordering. Using this characterization, we show that for a reflexive digraph$H$ which does not admit a Min-Max ordering, the minimum cost homomorphism problem is NP-complete. Thus we obtain a full dichotomy classification of the complexity of minimum cost homomorphism problems for reflexive digraphs

The effect of life skills training on the educational stress deduction of the Islamic Azad university students in 2013-2014

This article aims to determine the level of life skills training effect on the educational stress of the Islamic Azad University students of Sanandaj in 2013-2014 and it was done by using the experimental research method with pre-test and post-test of interviewed (testifier) group. The statistic society of this article consist of all Islamic Azad University students of Sanandaj in 2013-2014 that based on statistics it was about 11000 persons that Cochran's model was used for estimating the sample size and 277 persons were chosen casually. According to the sample size, firstly the student life stress questionnaire was performed and 60 persons of people that had maximum students life stress depend on questionnaire scale were chosen and screened. The 60 screened persons were divided into two experimental group and control group. It means that 30 people in the experimental group that was taken under the life skills training and 30 people as Control group in order to being compared with the experimental group in the terms of life skills training effect of the educational stress. For surveying the variable s relation, analysis statics and independent T test were used. The result showed that in the terms of life skills training effect on educational stress (there is a meaningful difference between the experimental group and control group) or in other hand, life skills had meaningful effect on the educational stress deduction