Distance-Regular Graphs

The introduction of intelligent devices with short range wireless communication techniques has motivated the development of Mobile Ad hoc NETworks (MANETs) during the last few years. However, traditional end-to-end based routing algorithms designed for MANETs are not much robust in the challenged networks suffering from frequent disruption, sparse network density and limited device capability. Such challenged networks, also known as Intermittently Connected Networks (ICNs) adopt the Store-Carry-Forward (SCF) behavior arising from the mobility of mobile nodes for message relaying. In this article, we consider the term ICNs as Delay/Disruption Tolerant Networks (DTNs) for the purpose of generalization, since DTNs have been envisioned for different applications with a large number of proposed routing algorithms. Motivated by the great interest from the research community, we firstly review the existing unicasting issue of DTNs because of its extensive research stage. Then, we also address multicasting and anycasting issues in DTNs considering their perspectives. A detail survey based on our taxonomy over the period from 2006 to 2010 is not only provided but also a comparison is given. We further identify the remaining challenges and open issues followed by an evaluation framework proposed for routing in DTNs. Finally, we summarize our contribution with three future research topics highlighted.

Routing in Delay/Disruption Tolerant Networks: A Taxonomy, Survey and Challenges

Nowadays, wireless networks are witnessing several deployments in various extreme environments where they suffer from different levels of link disruptions depending on the severity of the operating conditions. In all cases, their operation requirements are differently altered and their performance is negatively affected rendering them heterogeneous by nature. In the open literature, these networks are known as Intermittently Connected Networks (ICNs). The existing Internet protocols fail to operate properly in the context of ICNs, thus raising a variety of new challenging problems that are attracting the attention of the networking research community. Delay-/Disruption-Tolerant Networking emerged as a highly active area of research where networking experts compete in addressing the various ICN problems. Over time, unicast routing, one of the architectural key components common to all ICNs, became an almost independent field of research in which significant efforts continue to be invested. In contrast, network architectural designs, scheduling and forwarding issues dating from the early days of Inter-Planetary Networks (IPNs) have received relatively little attention and accumulate numerous pending challenges. Moreover, the gap caused by the lack of accurate ICN mathematical models is still large irrespective of some of the appreciated seminal works in this direction. This paper sheds the light over the latest advancements in each of the above-mentioned research sectors and highlight pending open issues in each of them.

Disruption-Tolerant Networking: A Comprehensive Survey on Recent Developments and Persisting Challenges

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.

The History of Degenerate (Bipartite) Extremal Graph Problems

3 Centralized CDS Construction 335 3.1 Guha and Khuller’s Algorithm . . . . . . . . . . . . . . . . . . . . . 336 3.2 Ruan’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 3.3 Cheng’s Greedy Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 340 3.4 Min’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 3.5 Butenko’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 341

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Connected Dominating Set in Sensor Networks and MANETs

We consider the problem of finding a large or dense triangle-free subgraph in a given graph G. In response to a question of P. Erdős, we prove that, if the minimum degree of G is at least 9|V (G)|/10, the largest triangle-free subgraphs are precisely the largest bipartite subgraphs in G. We investigate in particular the case where G is a complete multipartite graph. We prove that a finite tripartite graph with all edge densities greater than the golden ratio has a triangle and that this bound is best possible. Also we show that an infinite-partite graph with finite parts has a triangle, provided that the edge density between any two parts is greater than 1/2.

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Density Conditions For Triangles In Multipartite Graphs

Directed Triangles in Digraphs

On the girth of digraphs

On the largest eigenvalue of non-regular graphs

This paper studies the algorithmic issues of the spanning star forest problem. We prove the following results: (1) There is a polynomial-time approximation scheme for planar graphs; (2) there is a polynomial-time $\frac{3}{5}$-approximation algorithm for graphs; (3) it is NP-hard to approximate the problem within ratio $\frac{259}{260} + \epsilon$ for graphs; (4) there is a linear-time algorithm to compute the maximum star forest of a weighted tree; (5) there is a polynomial-time $\frac{1}{2}$-approximation algorithm for weighted graphs. We also show how to apply this spanning star forest model to aligning multiple genomic sequences over a tandem duplication region.

Jian Shen

Papers

Density Conditions For Triangles In Multipartite Graphs

Directed Triangles in Digraphs

On the girth of digraphs

On the largest eigenvalue of non-regular graphs

Approximating the Spanning Star Forest Problem and Its Application to Genomic Sequence Alignment