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A new and fast approximation algorithm for vertex cover using a maximum independent set (VCUMI)

100%

Khan I. , Riaz N.

Operations Research and Decisions

2015

tom Vol. 25, No. 4

5--18

The importance of non-deterministic polynomial (NP) problems in real world scenarios has compelled researchers to consider simple ways of finding approximate solutions to these problems in polynomial time. Minimum vertex cover is an NP complete problem, where the objective is to cover all the edges in a graph with the minimal number of vertices possible. The maximal independent set and maximal clique problems also belong to the same class. An important property that we have analyzed while considering various approaches to find approximate solutions to the minimum vertex cover problem (MVC) is that solving MVC directly can result in a bigger error ratio. We propose a new approximation algorithm for the minimum vertex cover problem called vertex cover using a maximum independent set (VCUMI). This algorithm works by removing the nodes of a maximum independent set until the graph is an approximate solution of MVC. Based on empirical results, it can be stated that VCUMI outperforms all competing algorithms presented in the literature. Based on all the benchmarks used, VCUMI achieved the worst case error ratio of 1.033, while VSA, MDG and NOVAC-1 gave the worst error ratios of 1.583, 1.107 and 1.04, respectively.

Lipoxygenase Inhibitory Lignans from Salvia santolinifolia

70%

Mehmood S. , Riaz N. , Ahmad Z. , Afza N. , Malik A.

Polish Journal of Chemistry

2008

tom Vol. 82, nr 3

571-575

Santolinol, a new lignan has been isolated from the chloroform soluble fraction of Salvia santolinifolia and as signed the structure 1 on the basis of spectral studies including 2D NMR. In addition three bifuranolignans namely didemethylpinoresinol 2, (+) fraxiresinol 3 and (+) 1-hydroxysyringaresinol 4 have also been isolated for the first time from this species. All these compounds showed potent inhibitory potential against the enzyme lipoxygenase.

Urease Inhibiting Guaianolides from Amberboa ramosa

51%

Khan S. , Riaz N. , Afza N. , Malik A. , Azhar-ul-Haq , Ahmed Z. , Lodhi M. , Choudhary M.

Polish Journal of Chemistry

2004

tom Vol.78 /nr 11-12

2075-2080

New sesquiterpene lactones have been isolated from the chloroform-soluble fraction of Amberboa ramosa and assigned two structures 4 beta-(chloromethyl)-3 beta, 4 alfa-dihydroxy, 8alfa-[(s)-2-carboxypropionoxy]-1alfaH,5alfaH,6betaH,7alfaH-guaia-10(14),11(13)-dien- 6,12-olide (1) and 4 beta(chloromethyl)-3beta ,4alfa-dihydroxy,8alfa-[(s)-3-hydroxy-2-methylpropionyloxy]- 1alfaH,5alfaH,6beta H,7alfaH-guaia-10(14),11(13)-dien-6,12-olide (2), respectively. In addition 5-hydroxy-6-methyl-7-methoxyflavone (3), 6,2',5'-trihydroxy-3,5,7-trimethoxyflavone (4) and 5-hydroxy-3,7,8,2'-tetramethoxyflavone (5) have also been reported for the first time from this species. Compounds 1 and 2 displayed promising inhibitory potential against enzyme urease in a concentration-dependent fashion.

In vivo antioxidant potential of Raphanus sativus seeds in rat kidney against CCl4-induced toxicity

36%

Shehzadi I. , Shah N. A. , Khan M. R. , Shuaib M. , Shah M. , Khan A. , Mohammed Ali H. S. H. , Anwar Y. , Hussain F. , Khan H. , Khan I. A. , Kaleem I. , Shabbir A. , Riaz N. , Haq A. , Rasheed Y. , Khan M. , Sher A. , Ali I. , Shaheen G.

Polish Journal of Environmental Studies

2020

tom 29

nr 1