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Sh. Habibi - One of the best experts on this subject based on the ideXlab platform.
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The Zariski Topology-Graph of modules over commutative rings II
Arabian Journal of Mathematics, 2020Co-Authors: Habibollah Ansari-toroghy, Sh. HabibiAbstract:Let M be a module over a commutative ring R. In this paper, we continue our study about the Zariski Topology-Graph $$G(\tau _T)$$ which was introduced in Ansari-Toroghy et al. (Commun Algebra 42:3283–3296, 2014). For a non-empty subset T of $$\mathrm{Spec}(M)$$ , we obtain useful characterizations for those modules M for which $$G(\tau _T)$$ is a bipartite Graph. Also, we prove that if $$G(\tau _T)$$ is a tree, then $$G(\tau _T)$$ is a star Graph. Moreover, we study coloring of Zariski Topology-Graphs and investigate the interplay between $$\chi (G(\tau _T))$$ and $$\omega (G(\tau _T))$$ .
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The Zariski Topology-Graph of modules over commutative rings II
Arabian Journal of Mathematics, 2020Co-Authors: Habibollah Ansari-toroghy, Sh. HabibiAbstract:Let M be a module over a commutative ring R . In this paper, we continue our study about the Zariski Topology-Graph $$G(\tau _T)$$ G ( τ T ) which was introduced in Ansari-Toroghy et al. (Commun Algebra 42:3283–3296, 2014). For a non-empty subset T of $$\mathrm{Spec}(M)$$ Spec ( M ) , we obtain useful characterizations for those modules M for which $$G(\tau _T)$$ G ( τ T ) is a bipartite Graph. Also, we prove that if $$G(\tau _T)$$ G ( τ T ) is a tree, then $$G(\tau _T)$$ G ( τ T ) is a star Graph. Moreover, we study coloring of Zariski Topology-Graphs and investigate the interplay between $$\chi (G(\tau _T))$$ χ ( G ( τ T ) ) and $$\omega (G(\tau _T))$$ ω ( G ( τ T ) ) .
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The Zariski Topology-Graph of modules over commutative rings II.
arXiv: Commutative Algebra, 2020Co-Authors: Habibollah Ansari-toroghy, Sh. HabibiAbstract:Let $M$ be a module over a commutative ring $R$. In this paper, we continue our study about the Zariski Topology-Graph $G(\tau_T)$ which was introduced in (The Zariski Topology-Graph of modules over commutative rings, Comm. Algebra., 42 (2014), 3283--3296). For a non-empty subset $T$ of $Spec(M)$, we obtain useful characterizations for those modules $M$ for which $G(\tau_T)$ is a bipartite Graph. Also, we prove that if $G(\tau_T)$ is a tree, then $G(\tau_T)$ is a star Graph. Moreover, we study coloring of Zariski Topology-Graphs and investigate the interplay between $\chi(G(\tau_T))$ and $\omega(G(\tau_T))$.
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The Zariski Topology-Graph of Modules Over Commutative Rings
Communications in Algebra, 2014Co-Authors: Habibollah Ansari-toroghy, Sh. HabibiAbstract:Let M be a module over a commutative ring, and let Spec(M) be the collection of all prime submodules of M. We topologize Spec(M) with Zariski Topology, which is analogous to that for Spec(R), and for a nonempty subset T of Spec(M), we introduce a new Graph G(τ T ), called the Zariski Topology-Graph. This Graph helps us to study the algebraic (resp. topological) properties of M (resp. Spec(M)) by using the Graph theoretical tools.
Habibollah Ansari-toroghy - One of the best experts on this subject based on the ideXlab platform.
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The Zariski Topology-Graph of modules over commutative rings II
Arabian Journal of Mathematics, 2020Co-Authors: Habibollah Ansari-toroghy, Sh. HabibiAbstract:Let M be a module over a commutative ring R. In this paper, we continue our study about the Zariski Topology-Graph $$G(\tau _T)$$ which was introduced in Ansari-Toroghy et al. (Commun Algebra 42:3283–3296, 2014). For a non-empty subset T of $$\mathrm{Spec}(M)$$ , we obtain useful characterizations for those modules M for which $$G(\tau _T)$$ is a bipartite Graph. Also, we prove that if $$G(\tau _T)$$ is a tree, then $$G(\tau _T)$$ is a star Graph. Moreover, we study coloring of Zariski Topology-Graphs and investigate the interplay between $$\chi (G(\tau _T))$$ and $$\omega (G(\tau _T))$$ .
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The Zariski Topology-Graph of modules over commutative rings II
Arabian Journal of Mathematics, 2020Co-Authors: Habibollah Ansari-toroghy, Sh. HabibiAbstract:Let M be a module over a commutative ring R . In this paper, we continue our study about the Zariski Topology-Graph $$G(\tau _T)$$ G ( τ T ) which was introduced in Ansari-Toroghy et al. (Commun Algebra 42:3283–3296, 2014). For a non-empty subset T of $$\mathrm{Spec}(M)$$ Spec ( M ) , we obtain useful characterizations for those modules M for which $$G(\tau _T)$$ G ( τ T ) is a bipartite Graph. Also, we prove that if $$G(\tau _T)$$ G ( τ T ) is a tree, then $$G(\tau _T)$$ G ( τ T ) is a star Graph. Moreover, we study coloring of Zariski Topology-Graphs and investigate the interplay between $$\chi (G(\tau _T))$$ χ ( G ( τ T ) ) and $$\omega (G(\tau _T))$$ ω ( G ( τ T ) ) .
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The Zariski Topology-Graph of modules over commutative rings II.
arXiv: Commutative Algebra, 2020Co-Authors: Habibollah Ansari-toroghy, Sh. HabibiAbstract:Let $M$ be a module over a commutative ring $R$. In this paper, we continue our study about the Zariski Topology-Graph $G(\tau_T)$ which was introduced in (The Zariski Topology-Graph of modules over commutative rings, Comm. Algebra., 42 (2014), 3283--3296). For a non-empty subset $T$ of $Spec(M)$, we obtain useful characterizations for those modules $M$ for which $G(\tau_T)$ is a bipartite Graph. Also, we prove that if $G(\tau_T)$ is a tree, then $G(\tau_T)$ is a star Graph. Moreover, we study coloring of Zariski Topology-Graphs and investigate the interplay between $\chi(G(\tau_T))$ and $\omega(G(\tau_T))$.
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Domination number in the annihilating-submodule Graph of modules over commutative rings
arXiv: Commutative Algebra, 2020Co-Authors: Habibollah Ansari-toroghy, Shokoufeh HabibiAbstract:Let $M$ be a module over a commutative ring $R$. The annihilating-submodule Graph of $M$, denoted by $AG(M)$, is a simple Graph in which a non-zero submodule $N$ of $M$ is a vertex if and only if there exists a non-zero proper submodule $K$ of $M$ such that $NK=(0)$, where $NK$, the product of $N$ and $K$, is denoted by $(N:M)(K:M)M$ and two distinct vertices $N$ and $K$ are adjacent if and only if $NK=(0)$. This Graph is a submodule version of the annihilating-ideal Graph and under some conditions, is isomorphic with an induced subGraph of the Zariski Topology-Graph $G(\tau_T)$ which was introduced in (The Zariski Topology-Graph of modules over commutative rings, Comm. Algebra., 42 (2014), 3283--3296). In this paper, we study the domination number of $AG(M)$ and some connections between the Graph-theoretic properties of $AG(M)$ and algebraic properties of module $M$.
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The quasi-Zariski Topology-Graph on the maximal spectrum of modules over commutative rings
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2018Co-Authors: Habibollah Ansari-toroghy, Shokoufeh HabibiAbstract:AbstractLet M be a module over a commutative ring and let Max(M) be the collection of all maximal submodules of M. We topologize Max(M) with quasi-Zariski Topology, where M is a Max-top module. For a subset T of Max(M), we introduce a new Graph $G(\tau_T^{*m})$, called the quasi-Zariski Topology-Graph on the maximal spectrum of M. It helps us to study algebraic (resp. topological) properties of M (resp. Max(M)) by using the Graphs theoretical tools.
Ying Cai - One of the best experts on this subject based on the ideXlab platform.
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IPCCC - A subscription overlay network for large-scale and cost-efficient any source multicast
30th IEEE International Performance Computing and Communications Conference, 2011Co-Authors: Patricio Galdames, Qinghua Zheng, Ying CaiAbstract:This paper presents a subscription-based overlay network that supports efficient any-source multicast. The system lets users register to a central server and allows the server to incrementally build a Topology Graph that contains the network connections among the subscribers. With this Topology Graph in place, we address the challenges of minimizing network traffic and the delay incurred in broadcasting a data packet to all active subscribers. The active subscribers are organized in a directional ring, and for each of them, we find a number of predecessors and successors, the number of which depends on the subscriber's network capacity. When a node sends a packet, the packet is routed along the ring and to its successors simultaneously. To minimize the delay in data forwarding, we take network proximity into consideration when constructing ring and selecting a subscriber's successors and predecessors. In addition to being Topology-aware, the proposed system also features leveraging idling nodes for data forwarding. More specifically, the subscribers who are online but not participating in application services (e.g., gaming) are recruited to reduce network traffic and further reduce data latency.
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An Overlay Subscription Network for Live Internet TV Broadcast
IEEE Transactions on Knowledge and Data Engineering, 2006Co-Authors: Ying Cai, J. ZhouAbstract:We propose a framework, called overlay subscription network (OSN), for live Internet TV broadcast, where a subscriber can choose to watch at any time. This framework allows the source server to incrementally build a Topology Graph that contains the network connections not only from the server to each subscriber, but also among the subscribers themselves. With such a Topology Graph in place, we consider efficient overlay multicast for scalable OSN services. We first show that idling nodes, which do not receive video data for their own playback, can actually be used for data forwarding to significantly reduce the cost of overlay multicast. In light of this observation, we then propose a novel overlay multicast technique that distinguishes itself from existing schemes with these three aspects. First, the proposed technique is centered on the Topology Graph and can take advantage of the actual network connections among the subscribing nodes. Second, the new scheme is able to find and incorporate appropriate idling nodes in multicast to reduce network traffic. Third, with our approach, a node can be used in multiple multicast trees for data forwarding to improve the overall system performance. We evaluate the performance of the proposed technique through simulation. Our extensive studies show that the proposed framework has the potential to enable the Internet, a vehicle up to date mainly for transferring text and image data, for large-scale and cost-effective TV broadcast
Patricio Galdames - One of the best experts on this subject based on the ideXlab platform.
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CRIWG - A Subscription Overlay Network for Large-Scale and Efficient File Parallel Downloading
Lecture Notes in Computer Science, 2015Co-Authors: Patricio Galdames, Claudio Gutierrez-soto, Cristopher BarrientosAbstract:This paper presents a subscription-based overlay network that supports file parallel downloading for cloud collaboration. First, our system lets users to register to a central server and allows this server to incrementally build a Topology Graph containing the network connections among the subscribers. With this Topology Graph in place, we plan to address the challenges of minimizing network traffic and choosing the best set of nodes storing a chosen file for parallel downloading. When a subscriber wants to access a chosen file stored in the cloud, our system obtains for her a list of nodes having this file. Nodes in this list, are sorted considering both their network distance to the subscriber and their workloads. Second, selecting those top nodes, a bandwidth-aware parallel downloading technique is executed. Finally, our proposed system also features leveraging idling nodes for file downloading. More specifically, the subscribers who are on-line but not participating in downloading are recruited to reduce both network traffic and average latency.
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IPCCC - A subscription overlay network for large-scale and cost-efficient any source multicast
30th IEEE International Performance Computing and Communications Conference, 2011Co-Authors: Patricio Galdames, Qinghua Zheng, Ying CaiAbstract:This paper presents a subscription-based overlay network that supports efficient any-source multicast. The system lets users register to a central server and allows the server to incrementally build a Topology Graph that contains the network connections among the subscribers. With this Topology Graph in place, we address the challenges of minimizing network traffic and the delay incurred in broadcasting a data packet to all active subscribers. The active subscribers are organized in a directional ring, and for each of them, we find a number of predecessors and successors, the number of which depends on the subscriber's network capacity. When a node sends a packet, the packet is routed along the ring and to its successors simultaneously. To minimize the delay in data forwarding, we take network proximity into consideration when constructing ring and selecting a subscriber's successors and predecessors. In addition to being Topology-aware, the proposed system also features leveraging idling nodes for data forwarding. More specifically, the subscribers who are online but not participating in application services (e.g., gaming) are recruited to reduce network traffic and further reduce data latency.
Byrav Ramamurthy - One of the best experts on this subject based on the ideXlab platform.
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a scalable approach for survivable virtual Topology routing in optical wdm networks
IEEE Journal on Selected Areas in Communications, 2007Co-Authors: Ajay Todimala, Byrav RamamurthyAbstract:The survivable virtual Topology routing problem is to route a virtual Topology Graph on a optical fiber physical Topology such that the virtual Topology remains connected when failures occur in the physical Topology. In this work we study the problem of survivable virtual Topology routing under single node/SRLG (Shared Risk Link Group) failure model. We prove that the survivable virtual Topology routing problem under node/SRLG failures is NP-complete. We present an improved integer linear programming (ILP) formulation for computing the survivable routing of a virtual Topology Graph. However, ILP is not scalable when the network size scales more than a few tens of nodes. In this work, we present sub-classes of Graphs which more accurately model an actual network and for which a survivable routing can be easily computed solving an ILP. We successfully computed the survivable routing of virtual topologies belonging to these sub-classes against link/SRLG failures for topologies of size up to 24 nodes.