Distributed Delay-Tolerant Strategies for Equality-Constraint Sum-Preserving Resource Allocation

This paper proposes two nonlinear dynamics to solve constrained distributed optimization problem for resource allocation over a multi-agent network. In this setup, coupling constraint refers to resource-demand balance which is preserved at all-times. The proposed solutions can address various model nonlinearities, for example, due to quantization and/or saturation. Further, it allows to reach faster convergence or to robustify the solution against impulsive noise or uncertainties. We prove convergence over weakly connected networks using convex analysis and Lyapunov theory. Our findings show that convergence can be reached for general sign-preserving odd nonlinearity. We further propose delay-tolerant mechanisms to handle general bounded heterogeneous time-varying delays over the communication network of agents while preserving all-time feasibility. This work finds application in CPU scheduling and coverage control among others. This paper advances the state-of-the-art by addressing (i) possible nonlinearity on the agents/links, meanwhile handling (ii) resource-demand feasibility at all times, (iii) uniform-connectivity instead of all-time connectivity, and (iv) possible heterogeneous and time-varying delays. To our best knowledge, no existing work addresses contributions (i)-(iv) altogether. Simulations and comparative analysis are provided to corroborate our contributions

Routing efficiency in wireless sensor-actor networks considering semi-automated architecture

Wireless networks have become increasingly popular and advances in wireless communications and electronics have enabled the development of different kind of networks such as Mobile Ad-hoc Networks (MANETs), Wireless Sensor Networks (WSNs) and Wireless Sensor-Actor Networks (WSANs). These networks have different kind of characteristics, therefore new protocols that fit their features should be developed. We have developed a simulation system to test MANETs, WSNs and WSANs. In this paper, we consider the performance behavior of two protocols: AODV and DSR using TwoRayGround model and Shadowing model for lattice and random topologies. We study the routing efficiency and compare the performance of two protocols for different scenarios. By computer simulations, we found that for large number of nodes when we used TwoRayGround model and random topology, the DSR protocol has a better performance. However, when the transmission rate is higher, the routing efficiency parameter is unstable.Peer ReviewedPostprint (published version

A Study on Graph Coloring and Digraph Connectivity

This dissertation focuses on coloring problems in graphs and connectivity problems in digraphs. We obtain the following advances in both directions.;1. Results in graph coloring. For integers k,r \u3e 0, a (k,r)-coloring of a graph G is a proper coloring on the vertices of G with k colors such that every vertex v of degree d( v) is adjacent to vertices with at least min{lcub}d( v),r{rcub} different colors. The r-hued chromatic number, denoted by chir(G ), is the smallest integer k for which a graph G has a (k,r)-coloring.;For a k-list assignment L to vertices of a graph G, a linear (L,r)-coloring of a graph G is a coloring c of the vertices of G such that for every vertex v of degree d(v), c(v)∈ L(v), the number of colors used by the neighbors of v is at least min{lcub}dG(v), r{rcub}, and such that for any two distinct colors i and j, every component of G[c --1({lcub}i,j{rcub})] must be a path. The linear list r-hued chromatic number of a graph G, denoted chiℓ L,r(G), is the smallest integer k such that for every k-list L, G has a linear (L,r)-coloring. Let Mad( G) denotes the maximum subgraph average degree of a graph G. We prove the following. (i) If G is a K3,3-minor free graph, then chi2(G) ≤ 5 and chi3(G) ≤ 10. Moreover, the bound of chi2( G) ≤ 5 is best possible. (ii) If G is a P4-free graph, then chir(G) ≤q chi( G) + 2(r -- 1), and this bound is best possible. (iii) If G is a P5-free bipartite graph, then chir( G) ≤ rchi(G), and this bound is best possible. (iv) If G is a P5-free graph, then chi2(G) ≤ 2chi(G), and this bound is best possible. (v) If G is a graph with maximum degree Delta, then each of the following holds. (i) If Delta ≥ 9 and Mad(G) \u3c 7/3, then chiℓL,r( G) ≤ max{lcub}lceil Delta/2 rceil + 1, r + 1{rcub}. (ii) If Delta ≥ 7 and Mad(G)\u3c 12/5, then chiℓ L,r(G)≤ max{lcub}lceil Delta/2 rceil + 2, r + 2{rcub}. (iii) If Delta ≥ 7 and Mad(G) \u3c 5/2, then chi ℓL,r(G)≤ max{lcub}lcei Delta/2 rceil + 3, r + 3{rcub}. (vi) If G is a K 4-minor free graph, then chiℓL,r( G) ≤ max{lcub}r,lceilDelta/2\rceil{rcub} + lceilDelta/2rceil + 2. (vii) Every planar graph G with maximum degree Delta has chiℓL,r(G) ≤ Delta + 7.;2. Results in digraph connectivity. For a graph G, let kappa( G), kappa\u27(G), delta(G) and tau( G) denote the connectivity, the edge-connectivity, the minimum degree and the number of edge-disjoint spanning trees of G, respectively. Let f(G) denote kappa(G), kappa\u27( G), or Delta(G), and define f¯( G) = max{lcub}f(H): H is a subgraph of G{rcub}. An edge cut X of a graph G is restricted if X does not contain all edges incident with a vertex in G. The restricted edge-connectivity of G, denoted by lambda2(G), is the minimum size of a restricted edge-cut of G. We define lambda 2(G) = max{lcub}lambda2(H): H ⊂ G{rcub}.;For a digraph D, let kappa;(D), lambda( D), delta--(D), and delta +(D) denote the strong connectivity, arc-strong connectivity, minimum in-degree, and out-degree of D, respectively. For each f ∈ {lcub}kappa,lambda, delta--, +{rcub}, define f¯(D) = max{lcub} f(H): H is a subdigraph of D{rcub}.;Catlin et al. in [Discrete Math., 309 (2009), 1033-1040] proved a characterization of kappa\u27(G) in terms of tau(G). We proved a digraph version of this characterization by showing that a digraph D is k-arc-strong if and only if for any vertex v in D, D has k-arc-disjoint spanning arborescences rooted at v. We also prove a characterization of uniformly dense digraphs analogous to the characterization of uniformly dense undirected graphs in [Discrete Applied Math., 40 (1992) 285--302]. (Abstract shortened by ProQuest.)