On the complexity of strongly connected components in directed hypergraphs

We study the complexity of some algorithmic problems on directed hypergraphs and their strongly connected components (SCCs). The main contribution is an almost linear time algorithm computing the terminal strongly connected components (i.e. SCCs which do not reach any components but themselves). "Almost linear" here means that the complexity of the algorithm is linear in the size of the hypergraph up to a factor alpha(n), where alpha is the inverse of Ackermann function, and n is the number of vertices. Our motivation to study this problem arises from a recent application of directed hypergraphs to computational tropical geometry. We also discuss the problem of computing all SCCs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. Besides, we prove a linear time reduction from the well-studied problem of finding all minimal sets among a given family to the problem of computing the SCCs. Only subquadratic time algorithms are known for the former problem. These results strongly suggest that the problem of computing the SCCs is harder in directed hypergraphs than in directed graphs.Comment: v1: 32 pages, 7 figures; v2: revised version, 34 pages, 7 figure

Plantas com possível atividade hipolipidêmica: uma revisão bibliográfica de livros editados no Brasil entre 1998 e 2008 Plants with possible hypolipidemic activity: a review of books published in Brazil between 1998 and 2008

O objetivo deste trabalho foi realizar levantamento sobre as plantas medicinais indicadas para o tratamento da hiperlipidemia, hipercolesterolemia e/ou aterosclerose. Este estudo foi feito a partir da pesquisa bibliográfica em 32 livros publicados no Brasil entre 1998 e 2008, resultando em lista de 85 espécies distribuídas em 53 famílias, principalmente Asteraceae e Fabaceae, com 54 espécies exóticas e 31 nativas. As espécies mais citadas foram Allium sativum (Alliaceae), Cynara scolymus (Asteraceae), Curcuma longa (Zingiberaceae), Allium cepa (Alliaceae), Echinodorus grandiflorus (Alismataceae), Taraxacum officinale (Asteraceae), Vernonia condensata (Asteraceae), Cuphea carthagenensis (Lythraceae) e Curcuma zedoaria (Zingiberaceae). As espécies nativas, citadas em pelo menos 2 livros, foram investigadas para alguma evidencia científica relacionada a possíveis efeitos hipolipidêmico, hipocolesterolêmico e/ou contra aterosclerose. Somente foram encontrados estudos científicos, relacionados a estes efeitos, para as espécies nativas Cuphea carthagenensis e Echinodorus grandiflorum, indicando a necessidade de pesquisas que possam garantir a segurança e a eficácia do uso destas espécies.<br>The aim of this study was to survey medicinal plants indicated for the treatment of hyperlipidemia, hypercholesterolemia and/or atherosclerosis. This study was performed from a review of 32 books published in Brazil between 1998 and 2008, resulting in a list of 85 species belonging to 53 families, especially Asteraceae and Fabaceae, with 54 exotic and 31 native species. The species most often cited were Allium sativum (Alliaceae), Cynara scolymus (Asteraceae), Curcuma longa (Zingiberaceae), Allium cepa (Alliaceae), Echinodorus grandiflorus (Alismataceae), Taraxacum officinale (Asteraceae), Vernonia condensata (Asteraceae), Cuphea carthagenensis (Lythraceae) and Curcuma zedoaria (Zingiberaceae). Native species cited in at least 2 books were investigated for some scientific evidence related to possible hypolipidemic and hypocholesterolemic effects and/or action against atherosclerosis. Scientific studies related to these effects were found only for the native species Cuphea carthagenensis and Echinodorus grandiflorum, indicating the need for studies capable of assuring the safety and the efficacy as to the use of these species