Spanning Tree Algorithm and Basic Internetworking Ch 3.1.5 &
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Transparent LAN Service Over Cable
Transparent LAN Service over Cable This document describes the Transparent LAN Service (TLS) over Cable feature, which enhances existing Wide Area Network (WAN) support to provide more flexible Managed Access for multiple Internet service provider (ISP) support over a hybrid fiber-coaxial (HFC) cable network. This feature allows service providers to create a Layer 2 tunnel by mapping an upstream service identifier (SID) to an IEEE 802.1Q Virtual Local Area Network (VLAN). Finding Feature Information Your software release may not support all the features documented in this module. For the latest feature information and caveats, see the release notes for your platform and software release. To find information about the features documented in this module, and to see a list of the releases in which each feature is supported, see the Feature Information Table at the end of this document. Use Cisco Feature Navigator to find information about platform support and Cisco software image support. To access Cisco Feature Navigator, go to http://tools.cisco.com/ITDIT/CFN/. An account on http:// www.cisco.com/ is not required. Contents • Hardware Compatibility Matrix for Cisco cBR Series Routers, page 2 • Prerequisites for Transparent LAN Service over Cable, page 2 • Restrictions for Transparent LAN Service over Cable, page 3 • Information About Transparent LAN Service over Cable, page 3 • How to Configure the Transparent LAN Service over Cable, page 6 • Configuration Examples for Transparent LAN Service over Cable, page 8 • Verifying the Transparent LAN Service over Cable Configuration, page 10 • Additional References, page 11 • Feature Information for Transparent LAN Service over Cable, page 12 Cisco Converged Broadband Routers Software Configuration Guide For DOCSIS 1 Transparent LAN Service over Cable Hardware Compatibility Matrix for Cisco cBR Series Routers Hardware Compatibility Matrix for Cisco cBR Series Routers Note The hardware components introduced in a given Cisco IOS-XE Release are supported in all subsequent releases unless otherwise specified. -
Strongly Connected Component
Graph IV Ian Things that we would talk about ● DFS ● Tree ● Connectivity Useful website http://codeforces.com/blog/entry/16221 Recommended Practice Sites ● HKOJ ● Codeforces ● Topcoder ● Csacademy ● Atcoder ● USACO ● COCI Term in Directed Tree ● Consider node 4 – Node 2 is its parent – Node 1, 2 is its ancestors – Node 5 is its sibling – Node 6 is its child – Node 6, 7, 8 is its descendants ● Node 1 is the root DFS Forest ● When we do DFS on a graph, we would obtain a DFS forest. Noted that the graph is not necessarily a tree. ● Some of the information we get through the DFS is actually very useful, such as – Starting time of a node – Finishing time of a node – Parent of the node Some Tricks Using DFS Order ● Suppose vertex v is ancestor(not only parent) of u – Starting time of v < starting time of u – Finishing time of v > starting time of u ● st[v] < st[u] <= ft[u] < ft[v] ● O(1) to check if ancestor or not ● Flatten the tree to store subtree information(maybe using segment tree or other data structure to maintain) ● Super useful !!!!!!!!!! Partial Sum on Tree ● Given queries, each time increase all node from node v to node u by 1 ● Assume node v is ancestor of node u ● sum[u]++, sum[par[v]]-- ● Run dfs in root dfs(v) for all child u dfs(u) d[v] = d[v] + d[u] Types of Edges ● Tree edges – Edges that forms a tree ● Forward edges – Edges that go from a node to its descendants but itself is not a tree edge. -
Ieee 802.1 for Homenet
IEEE802.org/1 IEEE 802.1 FOR HOMENET March 14, 2013 IEEE 802.1 for Homenet 2 Authors IEEE 802.1 for Homenet 3 IEEE 802.1 Task Groups • Interworking (IWK, Stephen Haddock) • Internetworking among 802 LANs, MANs and other wide area networks • Time Sensitive Networks (TSN, Michael David Johas Teener) • Formerly called Audio Video Bridging (AVB) Task Group • Time-synchronized low latency streaming services through IEEE 802 networks • Data Center Bridging (DCB, Pat Thaler) • Enhancements to existing 802.1 bridge specifications to satisfy the requirements of protocols and applications in the data center, e.g. • Security (Mick Seaman) • Maintenance (Glenn Parsons) IEEE 802.1 for Homenet 4 Basic Principles • MAC addresses are “identifier” addresses, not “location” addresses • This is a major Layer 2 value, not a defect! • Bridge forwarding is based on • Destination MAC • VLAN ID (VID) • Frame filtering for only forwarding to proper outbound ports(s) • Frame is forwarded to every port (except for reception port) within the frame's VLAN if it is not known where to send it • Filter (unnecessary) ports if it is known where to send the frame (e.g. frame is only forwarded towards the destination) • Quality of Service (QoS) is implemented after the forwarding decision based on • Priority • Drop Eligibility • Time IEEE 802.1 for Homenet 5 Data Plane Today • 802.1Q today is 802.Q-2011 (Revision 2013 is ongoing) • Note that if the year is not given in the name of the standard, then it refers to the latest revision, e.g. today 802.1Q = 802.1Q-2011 and 802.1D -
Understand Vlans, Wired Lans, and Wireless Lans
LESSON 1,2_B 98-366 Networking Fundamentals UnderstandUnderstand VLANs,VLANs, WiredWired LANs,LANs, andand WirelessWireless LANsLANs LESSON 1.2_B 98-366 Networking Fundamentals Lesson Overview In this lesson, you will review: Wired local area networks Wireless local area networks Virtual local area networks (VLANs) LESSON 1.2_B 98-366 Networking Fundamentals Anticipatory Set Explain why wireless networks are so popular, especially in homes Describe the elements that make up a wireless network What is the opposite of a wireless network? LESSON 1.2_B 98-366 Networking Fundamentals LAN A local area network (LAN) is a single broadcast domain. This means the broadcast will be received by every other user on the LAN if a user broadcasts information on his/her LAN. Broadcasts are prevented from leaving a LAN by using a router. Wired LAN An electronic circuit or hardware grouping in which the configuration is determined by the physical interconnection of the components LESSON 1.2_B 98-366 Networking Fundamentals Wireless LAN Communications that take place without the use of interconnecting wires or cables, such as by radio, microwave, or infrared light Wireless networks can be installed: o Peer-to-peer “Ad hoc” mode—wireless devices can communicate with each other o "Infrastructure" mode—allows wireless devices to communicate with a central node that can communicate with wired nodes on that LAN LESSON 1.2_B 98-366 Networking Fundamentals Sample example of a wireless LAN design: LESSON 1.2_B 98-366 Networking Fundamentals Wired LANs: Advantages Most wired LANs are built with inexpensive hardware: 1. Network adapter 2. Ethernet cables 3. -
CLRS B.4 Graph Theory Definitions Unit 1: DFS Informally, a Graph
CLRS B.4 Graph Theory Definitions Unit 1: DFS informally, a graph consists of “vertices” joined together by “edges,” e.g.,: example graph G0: 1 ···················•······························· ····························· ····························· ························· ···· ···· ························· ························· ···· ···· ························· ························· ···· ···· ························· ························· ···· ···· ························· ············· ···· ···· ·············· 2•···· ···· ···· ··· •· 3 ···· ···· ···· ···· ···· ··· ···· ···· ···· ···· ···· ···· ···· ···· ···· ···· ······· ······· ······· ······· ···· ···· ···· ··· ···· ···· ···· ···· ···· ··· ···· ···· ···· ···· ···· ···· ···· ···· ···· ···· ··············· ···· ···· ··············· 4•························· ···· ···· ························· • 5 ························· ···· ···· ························· ························· ···· ···· ························· ························· ···· ···· ························· ····························· ····························· ···················•································ 6 formally a graph is a pair (V, E) where V is a finite set of elements, called vertices E is a finite set of pairs of vertices, called edges if H is a graph, we can denote its vertex & edge sets as V (H) & E(H) respectively if the pairs of E are unordered, the graph is undirected if the pairs of E are ordered the graph is directed, or a digraph two vertices joined by an edge -
Graph Theory
1 Graph Theory “Begin at the beginning,” the King said, gravely, “and go on till you come to the end; then stop.” — Lewis Carroll, Alice in Wonderland The Pregolya River passes through a city once known as K¨onigsberg. In the 1700s seven bridges were situated across this river in a manner similar to what you see in Figure 1.1. The city’s residents enjoyed strolling on these bridges, but, as hard as they tried, no residentof the city was ever able to walk a route that crossed each of these bridges exactly once. The Swiss mathematician Leonhard Euler learned of this frustrating phenomenon, and in 1736 he wrote an article [98] about it. His work on the “K¨onigsberg Bridge Problem” is considered by many to be the beginning of the field of graph theory. FIGURE 1.1. The bridges in K¨onigsberg. J.M. Harris et al., Combinatorics and Graph Theory , DOI: 10.1007/978-0-387-79711-3 1, °c Springer Science+Business Media, LLC 2008 2 1. Graph Theory At first, the usefulness of Euler’s ideas and of “graph theory” itself was found only in solving puzzles and in analyzing games and other recreations. In the mid 1800s, however, people began to realize that graphs could be used to model many things that were of interest in society. For instance, the “Four Color Map Conjec- ture,” introduced by DeMorgan in 1852, was a famous problem that was seem- ingly unrelated to graph theory. The conjecture stated that four is the maximum number of colors required to color any map where bordering regions are colored differently. -
Vizing's Theorem and Edge-Chromatic Graph
VIZING'S THEOREM AND EDGE-CHROMATIC GRAPH THEORY ROBERT GREEN Abstract. This paper is an expository piece on edge-chromatic graph theory. The central theorem in this subject is that of Vizing. We shall then explore the properties of graphs where Vizing's upper bound on the chromatic index is tight, and graphs where the lower bound is tight. Finally, we will look at a few generalizations of Vizing's Theorem, as well as some related conjectures. Contents 1. Introduction & Some Basic Definitions 1 2. Vizing's Theorem 2 3. General Properties of Class One and Class Two Graphs 3 4. The Petersen Graph and Other Snarks 4 5. Generalizations and Conjectures Regarding Vizing's Theorem 6 Acknowledgments 8 References 8 1. Introduction & Some Basic Definitions Definition 1.1. An edge colouring of a graph G = (V; E) is a map C : E ! S, where S is a set of colours, such that for all e; f 2 E, if e and f share a vertex, then C(e) 6= C(f). Definition 1.2. The chromatic index of a graph χ0(G) is the minimum number of colours needed for a proper colouring of G. Definition 1.3. The degree of a vertex v, denoted by d(v), is the number of edges of G which have v as a vertex. The maximum degree of a graph is denoted by ∆(G) and the minimum degree of a graph is denoted by δ(G). Vizing's Theorem is the central theorem of edge-chromatic graph theory, since it provides an upper and lower bound for the chromatic index χ0(G) of any graph G. -
Superposition and Constructions of Graphs Without Nowhere-Zero K-flows
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Europ. J. Combinatorics (2002) 23, 281–306 doi:10.1006/eujc.2001.0563 Available online at http://www.idealibrary.com on Superposition and Constructions of Graphs Without Nowhere-zero k-flows M ARTIN KOCHOL Using multi-terminal networks we build methods on constructing graphs without nowhere-zero group- and integer-valued flows. In this way we unify known constructions of snarks (nontrivial cubic graphs without edge-3-colorings, or equivalently, without nowhere-zero 4-flows) and provide new ones in the same process. Our methods also imply new complexity results about nowhere-zero flows in graphs and state equivalences of Tutte’s 3- and 5-flow conjectures with formally weaker statements. c 2002 Elsevier Science Ltd. All rights reserved. 1. INTRODUCTION Nowhere-zero flows in graphs have been introduced by Tutte [38–40]. Primarily he showed that a planar graph is face-k-colorable if and only if it admits a nowhere-zero k-flow (its edges can be oriented and assigned values ±1,..., ±(k − 1) so that the sum of the incoming values equals the sum of the outcoming ones for every vertex of the graph). Tutte also proved the classical equivalence result that a graph admits a nowhere-zero k-flow if and only if it admits a flow whose values are the nonzero elements of a finite abelian group of order k. Seymour [35] has proved that every bridgeless graph admits a nowhere-zero 6-flow, thereby improving the 8-flow theorem of Jaeger [16] and Kilpatrick [20]. -
Finding Articulation Points and Bridges Articulation Points Articulation Point
Finding Articulation Points and Bridges Articulation Points Articulation Point Articulation Point A vertex v is an articulation point (also called cut vertex) if removing v increases the number of connected components. A graph with two articulation points. 3 / 1 Articulation Points Given I An undirected, connected graph G = (V; E) I A DFS-tree T with the root r Lemma A DFS on an undirected graph does not produce any cross edges. Conclusion I If a descendant u of a vertex v is adjacent to a vertex w, then w is a descendant or ancestor of v. 4 / 1 Removing a Vertex v Assume, we remove a vertex v 6= r from the graph. Case 1: v is an articulation point. I There is a descendant u of v which is no longer reachable from r. I Thus, there is no edge from the tree containing u to the tree containing r. Case 2: v is not an articulation point. I All descendants of v are still reachable from r. I Thus, for each descendant u, there is an edge connecting the tree containing u with the tree containing r. 5 / 1 Removing a Vertex v Problem I v might have multiple subtrees, some adjacent to ancestors of v, and some not adjacent. Observation I A subtree is not split further (we only remove v). Theorem A vertex v is articulation point if and only if v has a child u such that neither u nor any of u's descendants are adjacent to an ancestor of v. Question I How do we determine this efficiently for all vertices? 6 / 1 Detecting Descendant-Ancestor Adjacency Lowpoint The lowpoint low(v) of a vertex v is the lowest depth of a vertex which is adjacent to v or a descendant of v. -
(Rapid) Spanning Tree Protocol
STP – Spanning Tree Protocol indigoo.com STP & RSTP (RAPID) SPANNING TREE PROTOCOL DESCRIPTION OF STP AND RSTP, PROTOCOLS FOR LOOP FREE LAN TOPOLOGIES Peter R. Egli INDIGOO.COM1/57 © Peter R. Egli 2015 Rev. 1.60 STP – Spanning Tree Protocol indigoo.com Contents 1. Goal of STP: Loop-free topology for Ethernet networks 2. STP standards overview 3. IEEE 802.1D STP protocol 4. IEEE 802.1w RSTP Rapid STP 5. IEEE 802.1Q CST Common Spanning Tree 6. Cisco PVST+ and PVRST+ 7. IEEE 802.1s MST Multiple Spanning Tree Protocol 8. STP Pros and Cons 2/57 © Peter R. Egli 2015 Rev. 1.60 STP – Spanning Tree Protocol indigoo.com 1. Goal of STP: Loop-free topology for Ethernet networks Ethernet bridges (or switches) must forward unknown unicast and broadcast Ethernet frames to all physical ports. Therefore Ethernet networks require a loop-free topology, otherwise more and more broadcast and unknown unicast frames would swamp the network (creation of frame duplicates resulting in a broadcast storm). Unknown unicast frame: Frame with a target Ethernet address that is not yet known by the receiving bridge. Broadcast frame: Ethernet frame with a broadcast target Ethernet address, e.g. for protocols such as ARP or BOOTP / DHCP. Broadcast Ethernet frames and unknown unicast frames circle forever in an Ethernet network with loops. 3/57 © Peter R. Egli 2015 Rev. 1.60 STP – Spanning Tree Protocol indigoo.com 2. STP standards overview: A number of different STP ‘standards’ and protocols evolved over time. Standard Description Abbreviation Spanning Tree Protocol • Loop prevention. IEEE 802.1D • Automatic reconfiguration of tree in case of topology changes (e.g. -
Refs. 769001, 769002 Art
Refs. 769001, 769002 Art. Nr. WAVEDATAP, WAVEDATAS WaveData AP MyNETWiFi User Guide www.televes.com Table of Contents Important Safety Instructions ..................................................................................... 4 EN Introduction ................................................................................................................. 4 WaveData highlights .............................................................................................. 4 WaveData Package content .................................................................................. 5 Security Considerations ............................................................................................. 5 Operating Considerations .......................................................................................... 5 ENGLISH WaveData Device ........................................................................................................ 5 Port Connections .................................................................................................. 5 Device Buttons ...................................................................................................... 6 Device Leds ........................................................................................................... 6 Installing WaveData ..................................................................................................... 7 Installation example Ref.769001 .......................................................................... 7 Installation -
Sample Architecture for Avaya IP Telephony Solutions with Extreme Networks and Juniper Networks - Issue 1.0
Avaya Solution & Interoperability Test Lab Sample Architecture for Avaya IP Telephony Solutions with Extreme Networks and Juniper Networks - Issue 1.0 Abstract These Application Notes describe the configuration used for interoperability testing conducted between Avaya, Extreme Networks, Juniper Networks and Infoblox. The configuration consists of two locations, Site A and Site B, which were interconnected via serial links over a Wide Area Network (WAN). Testing included aspects of High Availability (HA) architecture, redundant design, Quality of Service (QoS) for voice communications, 802.11x port authentication and firewall Application Layer Gateway (ALG) security. The test cases were designed to confirm basic functionality amongst the vendors in the configuration at Layers 2 through 7. All test cases completed successfully. Information in these Application Notes has been obtained through compliance testing and additional technical discussions. Testing was conducted via the DeveloperConnection Program at the Avaya Solution & Interoperability Test Lab. GAK/SZ; Reviewed: Solution & Interoperability Test Lab Application Notes 1 of 47 SPOC 9/28/2005 ©2005 Avaya Inc. All Rights Reserved. aejarch.doc 1. Introduction The Application Notes provide a sample architecture demonstrating interoperability of products and solutions from Avaya, Extreme Networks, Juniper Networks and Infoblox. Figure 1 depicts the sample configuration. Figure 1: Sample Reference Architecture Configuration GAK/SZ; Reviewed: Solution & Interoperability Test Lab Application Notes 2 of 47 SPOC 9/28/2005 ©2005 Avaya Inc. All Rights Reserved. aejarch.doc An Avaya S8700 IP-Connect based system was used at Site A, depicted in Figure 2. Duplicated IP Server Interface (IPSI) circuit packs were used to provide “High” reliability to the two IPSI- connected G650 Media Gateways.