Organizing the atoms of the clique separator decomposition into an atom tree

International audienceWe define an atom tree of a graph as a generalization of a clique tree: its nodes are the atoms obtained by clique minimal separator decomposition, and its edges correspond to the clique minimal separators of the graph.Given a graph GG, we compute an atom tree by using a clique tree of a minimal triangulation HH of GG. Computing an atom tree with such a clique tree as input can be done in O(min(nm,m+nf))O(min(nm,m+nf)), where ff is the number of fill edges added by the triangulation. When both a minimal triangulation and the clique minimal separators of GG are provided, we compute an atom tree of GG in O(m+f)O(m+f) time, which is in O(n2)O(n2) time.We give an O(nm)O(nm) time algorithm, based on MCS, which combines in a single pass the 3 steps involved in building an atom tree: computing a minimal triangulation, constructing a clique tree, and constructing the corresponding atom tree.Finally, we present a process which uses a traversal of a clique tree of a minimal triangulation to determine the clique minimal separators and build the corresponding atom tree in O(n(n+t))O(n(n+t)) time, where tt is the number of 2-pairs of HH (tt is at most View the MathML sourcem¯−f, where View the MathML sourcem¯ is the number of edges of the complement graph); to complete this, we also give an algorithm which computes a minimal triangulation in View the MathML sourceO(n(n+m¯)) time, thus providing an approach to compute the decomposition in View the MathML sourceO(n(n+m¯)) time

The effects of macroeconomic variables and institutional qualities on stock prices : a panel data analysis

The unresolved dispute about the stochastic behaviour of the financial exchange, macroeconomic factors, and their cointegrating residuals continues. There is no consensus on the nature of the interaction between capital market returns and macroeconomic variables. This study aims to observe whether the institutional quality and macroeconomic variables individually and/or jointly contribute to the dynamic behaviour of the stock market. In particular, this study attempts to analyse the long run equilibrium and short-term dynamic relationship between the stock prices of developed and emerging markets and selected institutional quality and macroeconomic variables over the period between 1984 and 2019. The major outcome of this thesis is that it provides various empirical results on the bivariate and multivariate causality and cointegrating relationships between the share price index and macroeconomic and institutional quality variables of 21 developed and 9 emerging markets around the world. The major variables used in this study are Share Price Index (SPI), Real Gross Domestic Product (RGDP), Industrial Production Index (IPI), Consumer Price Index (CPI), Foreign Direct Investment (FDI), Workers’ Remittances (REMI), Real Effective Exchange Rate (REER). Trade Openness (OPEN), Interest Rate (IR), Corruption Risk Rating (CR), Government Stability (GS). This study also observed a known structural break in 2008 attributable to the global financial crisis (GFC), and a dummy variable DGFC is used to capture the impact of GFC on the share price indices. This study found that there exists cointegrating relationship among selected variables of developed markets. Emerging and developed markets combinedly demonstrated the same cointegration results, but emerging markets demonstrated no cointegrating relationship among variables. This study suggests that in developed markets, real GDP, industrial production, foreign direct investment, worker’s remittances, and real effective exchange rate positively influences the share price index in the long run. However, trade openness has a mixed influence on the share price index in the long run in developed markets. Similar results are found for emerging and developed markets combinedly in the existing literature. This study also finds that, in emerging markets, real GDP growth, FDI growth, REER growth, corruption risk rating, and government stability positively influence share price growth in the short run. But interest rate has a negative influence on share price growth in the short run