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Among the most fundamental graph parameters is the Diameter, the largest distance between any pair of vertices in a graph. Computing the Diameter of a graph with m edges requires m^2−o(1) time under the Strong Exponential Time Hypothesis (SETH), which ...

Among the most important graph parameters is the diameter, the largest distance between any two vertices. There are no known very efficient algorithms for computing the diameter exactly. Thus, much research has been devoted to how fast this parameter can ...

This paper presents efficient shared-memory parallel implementations and the first comprehensive experimental study of graph eccentricity estimation algorithms in the literature. The implementations include (1) a simple algorithm based on executing two-...

Using an intuition from metric geometry, we prove that any flag normal simplicial complex satisfies the nonrevisiting path conjecture. As a consequence, the diameter of its facet-ridge graph is smaller than the number of vertices minus the dimension, as ...

The diameter and the radius of a graph are fundamental topological parameters that have many important practical applications in real world networks. The fastest combinatorial algorithm for both parameters works by solving the all-pairs shortest paths ...

Average path length is recognised as one of the vital characteristics of random graphs and complex networks. Despite a rather sparse structure, some cases were reported to have a relatively short lengths between every pair of nodes, making the whole ...

Finding an optimal key assignment (subject to given constraints) for a key predistribution scheme in wireless sensor networks is a difficult task. Hence, most of the practical schemes are based on probabilistic key assignment, which leads to suboptimal ...

The diameter of a graph is among its most basic parameters. Since a few years ago, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones producing ...

In this paper, a fast algorithm is proposed to calculate kth power of an n × n Boolean matrix that requires O(kn³p) addition operations, where p is the probability that an entry of the matrix is 1. The algorithm generates a single set of inference rules ...

The increasing amount of data to be processed by computers has led to the need for highly efficient algorithms for various computational problems. Moreover, the algorithms should be as simple as possible to be practically applicable. In this paper we ...

In transportation and telecommunication systems, the performance of the underlying network can often be improved by upgrading some of the arcs in the network. If an arc is upgraded, the travel time along this arc is reduced by a discount factor α, 0 ≤ α ...

Among Cayley graphs on the symmetric group, some that have a noticeably low diameter relative to the number of generators involved are the pancake network, burnt pancake network and cycle prefix network. Another such Cayley graph is the star network, ...