The term combinatorial Gray code was introduced in 1980 to refer to any method for generating combinatorial objects so that successive objects differ in some prespecified, small way. This notion generalizes the classical binary reflected Gray code scheme for listing n-bit binary numbers so that successive numbers differ in exactly one bit position, as well as work in the 1960s and 1970s on minimal change listings for other combinatorial families, including permutations and combinations.
The area of combinatorial Gray codes was popularized by Herbert Wilf in his invited address at the SIAM Conference on Discrete Mathematics in 1988 and his subsequent SIAM monograph [Combinatorial Algorithms: An Update, 1989] in which he posed some open problems and variations on the theme. This resulted in much recent activity in the area, and most of the problems posed by Wilf are now solved.
In this paper, we survey the area of combinatorial Gray codes, describe recent results, variations, and trends, and highlight some open problems.

A Survey of Combinatorial Gray Codes

A system and method that provides for using source IP addresses and MAC addresses in a network to provide security against attempts by users of the network to use false source IP addresses in data packets. The system and method provide for analyzing MAC addresses and source IP addresses at the datalink (layer 2) level, and to use the information derived from such analysis to block access through a port where a host device is using a false, or spoofed, source IP address in transmitted data packets. Further, the system and method provide for validating initially learned source IP addresses, and for determining whether the number of unsuccessful attempts to validate new source IP addresses exceeds a threshold level, and where the number does exceed the threshold number the system and method can provide for operation in a possible attack mode.

System and method for source IP anti-spoofing security

A user authentication service for a communication network authenticates local users before granting them access to personalized sets of network resources. Authentication agents on intelligent edge devices present users of associated end systems with log-in challenges. Information supplied by the users is forwarded to an authentication server for verification. If successfully verified, the authentication server returns to the agents authorized connectivity information and time restrictions for the particular authenticated users. The agents use the information to establish rules for filtering and forwarding network traffic originating from or destined for particular authenticated users during authorized time periods. An enhanced authentication server may be engaged if additional security is desired. The authorized connectivity information preferably includes identifiers of one or more virtual local area networks active in the network. Log-in attempts are recorded so that the identity and whereabouts of network users may be monitored from a network management station.

Deterministic user authentication service for communication network

A platform and method of deploying virtual processing areas networks are described. A plurality of computer processors are connected to an internal communication network. At least one control node is in communication with an external communication network and an external storage network has an external storage address space. The at least one control node is connected to the internal network and thereby is in communication with the plurality of computer processors. Configuration logic defines and establishes a virtual processing area network having a corresponding set of computer processors from the plurality of processors, a virtual local area communication network providing communication among the set of computer processors, and a virtual storage space with a defined correspondence to the address space of the storage network.

Reconfigurable, virtual processing system, cluster, network and method

A router clustering system connects two or more routers to a one or more distinct Internet Service Providers (ISPs) in a complete high-availability arrangement. Typically the two or more routers connect to a plurality of ISPs at a site so that an outage of one ISP does not affect connectivity and availability to the site. The router clustering system typically includes a plurality of clustering units for redundancy that avoids difficulties that arise with a single point of failure. For example two clustering units may be used in an active-passive high-availability configuration. A router cluster creator creates or configures a router cluster. To create a router cluster, an administrator assigns to the cluster a logical Internet protocol (IP) address IPgw and specifies routers that are members of the cluster.

System and method for routing message traffic using a cluster of routers sharing a single logical IP address distinct from unique IP addresses of the routers

Provided are a method and system that allow one or more network protocol emulators, composed of one or more network protocol emulation controllers and one or more network protocol emulation entities, which are overlaid onto the one or more base networks utilizing different communications protocols for the purpose of allowing said one or more networks to be accessed and utilized as if the one or more networks were utilizing protocols emulated by the one or more network protocol emulators. The method and system utilize the following steps. Apprising the one or more network protocol emulation controllers of network capability information inherent within protocols utilized by the one or more networks onto which the one or more network protocol emulation controllers are overlaid. Directing that the one or more network emulation controllers utilize the one or more network capability information of which they have been apprised to define communication capabilities for certain network protocol emulation entities within the control of the one or more network protocol emulation controllers. Directing either the one or more network protocol emulation controllers or the one or more certain network protocol emulation entities within the control of the network protocol emulation controllers to utilize such defined communications capabilities to ensure that the network protocol emulation entities do not request a communications link to one or more other network protocol emulation entities that substantially exceeds the defined communication capabilities of the one or more other network protocol emulation entities.

Method for allowing more efficient communication in an environment wherein multiple protocols are utilized

An ELAN having redundant default gateways is attached to an asynchronous transfer mode (ATM) communications network. The ELAN's redundant default gateways are comprised of a first and second routers. The first router is associated with a primary default gateway and the second router is associated with a backup default gateway. Both the primary and backup default gateways are connected to the ELAN and both the primary and backup default gateways are configured with a default gateway IP address and associated MAC address. Initially, the primary default gateway registers the default gateway MAC address, thereby becoming the active default gateway. While the primary default gateway is active, the backup default gateway continually attempts to register the default gateway MAC address. When the primary default gateway fails, the backup default gateway will be able to successfully register the default gateway MAC address and take over the responsibilities of the primary default gateway and become the active default gateway.

Redundant internet protocol gateways using local area network emulation

A method is implemented to enable networks employing source-route bridging to participate in route switched, Asynchronous Transfer Mode (ATM), networks. Such source-routed networks, for example, Token-Ring LANs, incorporate an end-to-end route description in the data packets transmitted by the source station. The end-to-end route description is contained in a Route Information Field (RIF). The method implemented herein associates an RIF with the ATM address corresponding to a destination station. This permits the source-route bridged network to exploit the efficiencies of layer-2 connections and the high-speed switching characteristics of the ATM network.

Route switching mechanisms for source-routed ATM networks

A method and system for providing enhanced peer redundancy in an ATM emulated local area network (ELAN) served by a primary LAN emulation server (LES), a peer LAN emulation server, a broadcast and unknown server (BUS), and a LAN emulation configuration server (LECS). An enhanced peer redundancy virtual channel connection (VCC) is established between the primary LES/BUS and the peer LES/BUS. The primary LES/BUS and the peer LES/BUS exchange status messages every two seconds indicating the number of assigned LECs. If the primary has fewer LECs than the peer, the primary yields to the peer as the active LES/BUS. If an enhanced redundancy VCC was not established, the backup LES/BUS provides ELAN services while waiting for the primary to call to establish an enhanced redundancy VCC. If an enhanced peer redundancy VCC cannot be established, the primary attempts to establish a redundancy VCC with the peer in which the peer LES/BUS is kept in a dormant mode as long as the redundancy VCC is present. If the redundancy VCC is absent, the peer LES/BUS is activated to service the ELAN.

Method and system for providing peer redundancy to asynchronous transfer mode emulated local-area networks

For any $q \geq 2$, let $\Sigma_{q}=\{0,\ldots,q\!-\!1\}$, and fix a string $A$ over $\Sigma_{q}$. The $A$-free strings of length $n$ are the strings in $\Sigma_{q}^n$ which do not contain $A$ as a contiguous substring. In this paper, we investigate the possibility of listing the $A$-free strings of length $n$ so that successive strings differ in only one position, and by $\pm 1$ in that position. Such a listing is a Gray code for the $A$-free strings of length $n$. We identify those $q$ and $A$ such that, for infinitely many $n \geq 0$, a Gray code for the $A$-free strings of length $n$ is prohibited by a parity problem. Our parity argument uses techniques similar to those of Guibas and Odlyzko ( Journal of Combinatorial Theory A 30 (1981) pp. 183–208) who enumerated the $A$-free strings of length $n$. When $q$ is even, we also give the complementary positive result: for those $A$ for which an infinite number of parity problems do not exist, we construct a Gray code for the $A$-free strings of length $n$ for all $n \geq 0$.

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Matthew Blaze Squire

Papers

Method for allowing more efficient communication in an environment wherein multiple protocols are utilized

Redundant internet protocol gateways using local area network emulation

Route switching mechanisms for source-routed ATM networks

Method and system for providing peer redundancy to asynchronous transfer mode emulated local-area networks

Gray Codes for A-Free Strings