Flexural Fatigue performance of Alkali Activated Slag Concrete mixes incorporating Copper Slag as Fine Aggregate

The present investigation attempts a detailed study of mechanical properties and fatigue characteristics of a new class of Alkali Activated Slag Concrete (AASC) mixes incorporating Copper Slag (CS) as fine aggregates. The natural river sand is replaced with Copper Slag, upto 100% (by volume) as fine aggregate in these AASC mixes. The behavior of plain concrete prisms, cast with this range of AASC mixes under dynamic cyclic loads with sand/CS fine aggregates is studied and is compared with conventional OPC-based concrete specimens. The results indicate that incorporation of CS even upto 100% as fine aggregates, did not have any adverse effects on the mechanical properties of AASC mixes. The AASC mixes with CS displayed slightly better fatigue performance as compared to AASC mix with river sand. An attempt is also made herein to statistically describe the fatigue life data of AASC mixes using a 2-parameter Weibull distribution

A New Intersection Model and Improved Algorithms for Tolerance Graphs

Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This class of graphs, which generalizes in a natural way both interval and permutation graphs, has attracted many research efforts since their introduction in [M. C. Golumbic and C. L. Monma, Congr. Numer., 35 (1982), pp. 321–331], as it finds many important applications in constraint-based temporal reasoning, resource allocation, and scheduling problems, among others. In this article we propose the first non-trivial intersection model for general tolerance graphs, given by three-dimensional parallelepipeds, which extends the widely known intersection model of parallelograms in the plane that characterizes the class of bounded tolerance graphs. Apart from being important on its own, this new representation also enables us to improve the time complexity of three problems on tolerance graphs. Namely, we present optimal O(n log n) algorithms for computing a minimum coloring and a maximum clique and an O(n2) algorithm for computing a maximum weight independent set in a tolerance graph with n vertices, thus improving the best known running times O(n2) and O(n3) for these problems, respectively

The longest path problem is polynomial on cocomparability graphs

The longest path problem is the problem of finding a path of maximum length in a graph. As a generalization of the Hamiltonian path problem, it is NP-complete on general graphs and, in fact, on every class of graphs that the Hamiltonian path problem is NP-complete. Polynomial solutions for the longest path problem have recently been proposed for weighted trees, ptolemaic graphs, bipartite permutation graphs, interval graphs, and some small classes of graphs. Although the Hamiltonian path problem on cocomparability graphs was proved to be polynomial almost two decades ago [9], the complexity status of the longest path problem on cocomparability graphs has remained open until now; actually, the complexity status of the problem has remained open even on the smaller class of permutation graphs. In this paper, we present a polynomial-time algorithm for solving the longest path problem on the class of cocomparability graphs. Our result resolves the open question for the complexity of the problem on such graphs, and since cocomparability graphs form a superclass of both interval and permutation graphs, extends the polynomial solution of the longest path problem on interval graphs [18] and provides polynomial solution to the class of permutation graphs