Unpaired Many-to-Many Disjoint Path Cover of Balanced Hypercubes

A many-to-many [Formula: see text]-disjoint path cover ([Formula: see text]-DPC) of a graph [Formula: see text] is a set of [Formula: see text] vertex-disjoint paths joining [Formula: see text] distinct pairs of source and sink in which each vertex of [Formula: see text] is contained exactly once in a path. The balanced hypercube [Formula: see text], a variant of the hypercube, was introduced as a desired interconnection network topology. Let [Formula: see text] and [Formula: see text] be any two sets of vertices in different partite sets of [Formula: see text] ([Formula: see text]). Cheng et al. in [Appl. Math. Comput. 242 (2014) 127–142] proved that there exists paired many-to-many 2-disjoint path cover of [Formula: see text] when [Formula: see text]. In this paper, we prove that there exists unpaired many-to-many [Formula: see text]-disjoint path cover of [Formula: see text] ([Formula: see text]) from [Formula: see text] to [Formula: see text], which has improved some known results. The upper bound [Formula: see text] is best possible in terms of the number of disjoint paths in unpaired many-to-many [Formula: see text]-DPC of [Formula: see text].

SMGSAF: A Secure Multi-Geocasting based Routing Scheme for Opportunistic Networks

This paper proposes a novel Secure Multi- Geocasting Spray And Flood technique for opportunistic networks called SMGSAF, which uses secret sharing and disjoint path routing to secure the privacy of messages. In multi-geocasting, routing aims to successfully deliver a given geomessage to all the nodes, or to as many as possible, located inside defined geographic areas within a given time interval. It is desired that as long as a message is outside its destination casts it cannot be read by intermediate nodes. Encryption is a proven way to ensure this but classical encryption techniques are not well suited for the opportunistic paradigm. Key distribution and scarcity of resources are the major challenges in this regard. Therefore we have used secret sharing and disjoint path routing to protect the privacy of messages. Simulation results show that the proposed SMGSAF protocol provides the intended security but at the expense of performance, that is within acceptable limits. Notably, the SMGSAF protocol outperforms unitary geocasting in terms of delivery probability. The proposed protocol is evaluated in terms of delivery probability, network overhead, and latency. Its performance has been compared to MGSAF and GSAF.

Evaluating on Topology Survivability Based on Largest Number of Node-Disjoint Paths

<p>On the point of view of Largest Number of Node-Disjoint Path (LNNDP for short) between a node pair in a network, this article states the importance of LNNDP to global survivability of topology at first, then proposes an algorithm to compute maximal number of node-disjoint paths between node pairs. A new topology survivability metric based on LNNDP is put forward to evaluate the global survivability of network topology. It can be used to evaluate the survivability of topology provided. This metric can express accurately global topology survivability.</p>

Near-Optimal Disjoint-Path Facility Location Through Set Cover by Pairs

Content Distribution and End-to-End Monitoring with Set Cover by Pairs

Unpaired Many-to-Many Disjoint Path Covers on Bipartite k-Ary n-Cube Networks with Faulty Elements

The [Formula: see text]-ary [Formula: see text]-cube network is known as one of the most attractive interconnection networks for parallel and distributed systems. A many-to-many [Formula: see text]-disjoint path cover ([Formula: see text]-DPC for short) of a graph is a set of [Formula: see text] vertex-disjoint paths joining two disjoint vertex sets [Formula: see text] and [Formula: see text] of equal size [Formula: see text] that altogether cover every vertex of the graph. The many-to-many [Formula: see text]-DPC is classified as paired if each source in [Formula: see text] is further required to be paired with a specific sink in [Formula: see text], or unpaired otherwise. In this paper, we consider the unpaired many-to-many [Formula: see text]-DPC problem of faulty bipartite [Formula: see text]-ary [Formula: see text]-cube networks [Formula: see text], where the sets [Formula: see text] and [Formula: see text] are chosen in different parts of the bipartition. We show that, every bipartite [Formula: see text], under the condition that [Formula: see text] or less faulty edges are removed, has an unpaired many-to-many [Formula: see text]-DPC for any [Formula: see text] and [Formula: see text] subject to [Formula: see text]. The bound [Formula: see text] is tight here.