The Internet of Things (IoT) is emerging as an attractive paradigm, and several IoT models and related security issues have received widespread attentions. In this paper, we focus on an existing U2IoT architecture (i.e., Unit IoT and Ubiquitous IoT), and propose a directed path based authentication scheme (DPAS) to realize security protection for the U2IoT architecture. Particularly, the direct...

While standard persistent homology has been successful in extracting information from metric datasets, its applicability to more general data, e.g. directed networks, is hindered by its natural insensitivity to asymmetry. We study a construction of homology of digraphs due to Grigor’yan, Lin, Muranov and Yau, and extend this construction to the persistent framework. The result, which we call pe...

In the previous chapter, we saw algorithms to find the shortest path from a source vertex s to a target vertex t in a directed graph. As it turns out, the best algorithms for this problem actually find the shortest path from s to every possible target (or from every possible source to t) by constructing a shortest path tree. The shortest path tree specifies two pieces of information for each no...

SUMMARY An s-t ow in a directed network is called \un-controllable", when the ow is representable as a positive sum of elementary s-t path ows. In this paper, we discuss the problem \Is a given ow uncontrollable?". We show that the problem is NP-complete. 1. Introduction Recently, Iri proposed a new type of network ow theory [1], where only those ows which are representable as a positive sum of...

Given a digraph (an undirected graph, resp.) D and two positive integers f (x); g(x) for every x 2 V (D), a subgraph H of D is called a (g; f)-factor if g(x) d + H (x) = d ? H (x) f (x)(g(x) d H (x) f (x), resp.) for every x 2 V (D). If f (x) = g(x) = 1 for every x, then a connected (g; f)-factor is a hamiltonian cycle. The previous research related to the topic has been carried out either for ...

We consider semistructured data as multi rooted edge-labeled directed graphs, and path inclusion constraints on these graphs. A path inclusion constraint p q is satisfied by a semistructured data if any node reached by the regular query p is also reached by the regular query q. In this paper, two problems are mainly studied: the implication problem and the problem of the existence of a finite e...

Let D(n, p) be the random directed graph on n vertices where each of the n(n− 1) possible arcs is present independently with probability p. It is known that if p ≥ (log n+ ω(1))/n then D(n, p) typically has a directed Hamilton cycle, and this is best possible. We show that under the same condition, the number of directed Hamilton cycles in D(n, p) is typically n!(p(1 + o(1))) . We also prove a ...

We present an incomplete filtering algorithm for the circuit constraint. The filter removes redundant values by eliminating nonhamiltonian edges from the associated graph. We identify nonhamiltonian edges by analyzing a smaller graph with labeled edges that is defined on a separator of the original graph. The complexity of the procedure for each separator S is approximately O(|S|). We found tha...

In this paper, we explore the design of algorithms for the problem of checking whether an undirected graph contains a negative cost cycle (UNCCD). It is known that this problem is significantly harder than the corresponding problem in directed graphs. Current approaches for solving this problem involve reducing it to either the b-matching problem or the T -join problem. The latter approach is m...

An induced acyclic graphoidal cover of a graph G is a collection ψ of open paths in G such that every path in ψ has atleast two vertices, every vertex of G is an internal vertex of at most one path in ψ, every edge of G is in exactly one path in ψ and every member of ψ is an induced path. The minimum cardinality of an induced acyclic graphoidal cover of G is called the induced acyclic graphoida...