Algorithms for Self-Healing Networks

Many modern networks are \emph{reconfigurable}, in the sense that the topology of the network can be changed by the nodes in the network. For example, peer-to-peer, wireless and ad-hoc networks are reconfigurable. More generally, many social networks, such as a company's organizational chart; infrastructure networks, such as an airline's transportation network; and biological networks, such as the human brain, are also reconfigurable. Modern reconfigurable networks have a complexity unprecedented in the history of engineering, resembling more a dynamic and evolving living animal rather than a structure of steel designed from a blueprint. Unfortunately, our mathematical and algorithmic tools have not yet developed enough to handle this complexity and fully exploit the flexibility of these networks. We believe that it is no longer possible to build networks that are scalable and never have node failures. Instead, these networks should be able to admit small, and maybe, periodic failures and still recover like skin heals from a cut. This process, where the network can recover itself by maintaining key invariants in response to attack by a powerful adversary is what we call \emph{self-healing}. Here, we present several fast and provably good distributed algorithms for self-healing in reconfigurable dynamic networks. Each of these algorithms have different properties, a different set of gaurantees and limitations. We also discuss future directions and theoretical questions we would like to answer. %in the final dissertation that this document is proposed to lead to.

Self-healing systems and virtual structures

Modern networks are large, highly complex and dynamic. Add to that the mobility of the agents comprising many of these networks. It is difficult or even impossible for such systems to be managed centrally in an efficient manner. It is imperative for such systems to attain a degree of self-management. Self-healing i.e. the capability of a system in a good state to recover to another good state in face of an attack, is desirable for such systems. In this paper, we discuss the self-healing model for dynamic reconfigurable systems. In this model, an omniscient adversary inserts or deletes nodes from a network and the algorithm responds by adding a limited number of edges in order to maintain invariants of the network. We look at some of the results in this model and argue for their applicability and further extensions of the results and the model. We also look at some of the techniques we have used in our earlier work, in particular, we look at the idea of maintaining virtual graphs mapped over the existing network and assert that this may be a useful technique to use in many problem domains.

DEX: Self-Healing Expanders

We present a fully-distributed self-healing algorithm DEX, that maintains a constant degree expander network in a dynamic setting. To the best of our knowledge, our algorithm provides the first efficient distributed construction of expanders - whose expansion properties hold deterministically - that works even under an all-powerful adaptive adversary that controls the dynamic changes to the network (the adversary has unlimited computational power and knowledge of the entire network state, can decide which nodes join and leave and at what time, and knows the past random choices made by the algorithm). Previous distributed expander constructions typically provide only probabilistic guarantees on the network expansion which rapidly degrade in a dynamic setting, in particular, the expansion properties can degrade even more rapidly under adversarial insertions and deletions. Our algorithm provides efficient maintenance and incurs a low overhead per insertion/deletion by an adaptive adversary: only O(log n) rounds and O(log n) messages are needed with high probability (n is the number of nodes currently in the network). The algorithm requires only a constant number of topology changes. Moreover, our algorithm allows for an efficient implementation and maintenance of a distributed hash table (DHT) on top of DEX, with only a constant additional overhead. Our results are a step towards implementing efficient self-healing networks that have guaranteed properties (constant bounded degree and expansion) despite dynamic changes.

DEX: self-healing expanders

Compact Routing Messages in Self-Healing Trees

Existing compact routing schemes, e.g., Thorup and Zwick [SPAA 2001] and Chechik [PODC 2013], often have no means to tolerate failures, once the system has been setup and started. This paper presents, to our knowledge, the first self-healing compact routing scheme. Besides, our schemes are developed for low memory nodes, i.e., nodes need only O(log2 n) memory, and are thus, compact schemes.
We introduce two algorithms of independent interest: The first is CompactFT, a novel compact version (using only O(log n) local memory) of the self-healing algorithm Forgiving Tree of Hayes et al. [PODC 2008]. The second algorithm (CompactFTZ) combines CompactFT with Thorup-Zwick’s treebased compact routing scheme [SPAA 2001] to produce a fully compact self-healing routing scheme. In the self-healing model, the adversary deletes nodes one at a time with the affected nodes self-healing locally by adding few edges. CompactFT recovers from each attack in only O(1) time and ∆ messages, with only +3 degree increase and O(log∆) graph diameter increase, over any sequence of deletions (∆ is the initial maximum degree).
Additionally, CompactFTZ guarantees delivery of a packet sent from sender s as long as the receiver has not been deleted, with only an additional O(y log ∆) latency, where y is the number of nodes that have been deleted on the path between s and t. If t has been deleted, s gets informed and the packet removed from the network.

On-line self-healing of circuits implemented on reconfigurable FPGAs

To boost logic density and reduce per unit power consumption SRAM-based FPGAs manufacturers adopted nanometric technologies. However, this technology is highly vulnerable to radiation-induced faults, which affect values stored in memory cells, and to manufacturing imperfections. Fault tolerant implementations, based on Triple Modular Redundancy (TMR) infrastructures, help to keep the correct operation of the circuit. However, TMR is not sufficient to guarantee the safe operation of a circuit. Other issues like module placement, the effects of multi- bit upsets (MBU) or fault accumulation, have also to be addressed. In case of a fault occurrence the correct operation of the affected module must be restored and/or the current state of the circuit coherently re-established. A solution that enables the autonomous restoration of the functional definition of the affected module, avoiding fault accumulation, re-establishing the correct circuit state in real-time, while keeping the normal operation of the circuit, is presented in this paper.

A framework for self-healing radiation-tolerant implementations on reconfigurable FPGAs

To increase the amount of logic available in SRAM-based FPGAs manufacturers are using nanometric technologies to boost logic density and reduce prices. However, nanometric scales are highly vulnerable to radiation-induced faults that affect values stored in memory cells. Since the functional definition of FPGAs relies on memory cells, they become highly prone to this type of faults. Fault tolerant implementations, based on triple modular redundancy (TMR) infrastructures, help to keep the correct operation of the circuit. However, TMR is not sufficient to guarantee the safe operation of a circuit. Other issues like the effects of multi-bit upsets (MBU) or fault accumulation, have also to be addressed. Furthermore, in case of a fault occurrence the correct operation of the affected module must be restored and the current state of the circuit coherently re-established. A solution that enables the autonomous correct restoration of the functional definition of the affected module, avoiding fault accumulation, re-establishing the correct circuit state in realtime, while keeping the normal operation of the circuit, is presented in this paper.

A self-healing real-time system based on run-time self-reconfiguration

The new generations of SRAM-based FPGA (field programmable gate array) devices are the preferred choice for the implementation of reconfigurable computing platforms intended to accelerate processing in real-time systems. However, FPGA's vulnerability to hard and soft errors is a major weakness to robust configurable system design. In this paper, a novel built-in self-healing (BISH) methodology, based on run-time self-reconfiguration, is proposed. A soft microprocessor core implemented in the FPGA is responsible for the management and execution of all the BISH procedures. Fault detection and diagnosis is followed by repairing actions, taking advantage of the dynamic reconfiguration features offered by new FPGA families. Meanwhile, modular redundancy assures that the system still works correctly

A direct comparison of one- and two-component dendritic self-assembled materials: elucidating molecular recognition pathways

This paper compares and contrasts, for the first time, one- and two-component gelation systems that are direct structural analogues and draws conclusions about the molecular recognition pathways that underpin fibrillar self-assembly. The new one-component systems comprise L-lysine-based dendritic headgroups covalently connected to an aliphatic diamine spacer chain via an amide bond, One-component gelators with different generations of headgroup (from first to third generation) and different length spacer chains are reported. The self-assembly of these dendrimers in toluene was elucidated using thermal measurements, circular dichroism (CD) and NMR spectroscopies, scanning electron microscopy (SEM), and small-angle X-ray scattering (SAXS). The observations are compared with previous results for the analogous two-component gelation system in which the dendritic headgroups are bound to the aliphatic spacer chain noncovalently via acid-amine interactions. The one-component system is inherently a more effective gelator, partly as a consequence of the additional covalent amide groups that provide a new hydrogen bonding molecular recognition pathway, whereas the two-component analogue relies solely on intermolecular hydrogen bond interactions between the chiral dendritic headgroups. Furthermore, because these amide groups are important in the assembly process for the one-component system, the chiral information preset in the dendritic headgroups is not always transcribed into the nanoscale assembly, whereas for the two-component system, fiber formation is always accompanied by chiral ordering because the molecular recognition pathway is completely dependent on hydrogen bond interactions between well-organized chiral dendritic headgroups.

Self healing and self configuration in a WSRF grid environment

The move towards web services in Grid computing requires mechanisms for services to maintain state. This is introduced by the Web Services Resource Framework which provides a basis for web services to access stateful resources. While this allows access to stateful resources, the web services themselves are not stateful. Currently, Grids require a lot of direct involvement of application developers, who are, in general, not computing specialists. The principles of autonomic computing introduce characteristics which are aimed at automatic improvement of computing systems and can be applied to the Grid. This paper addresses the principles of self healing and self configuration in a Grid environment and implements a service using the WSRF.NET framework to investigate the affect and applicability of the Web Services Resource Framework on these principles and improve the WSRF specification.

Toward highly available, self-healing, adaptable, grid-like and user friendly nondedicated clusters

The human body was used to illustrate an Autonomic Computing system that possesses self-knowledge, self-configuration, self-optimization, self-healing, and self-protection, knowledge of its environment and user friendliness properties. Autonomic Computing was identified by IBM as one of the Grand Challenges. Many researchers and research groups have responded positively to the challenge by initiating research around one or two of the characteristics
identified by IBM as the requirements for Autonomic Computing. One of the areas that could benefit from the comprehensive approach created by the Autonomic Computing vision is parallel processing on nondedicated clusters. This paper shows a general design of services and initial implementation of a system that moves parallel processing on clusters to the computing mainstream using the Autonomic Computing vision.