An Implicit Optimization Approach for Survivable Network Design

We consider the problem of designing a network of minimum cost while satisfying a prescribed survivability criterion. The survivability criterion requires that a feasible flow must still exists (i.e. all demands can be satisfied without violating arc capacities) even after the disruption of a subset of the network's arcs. Specifically, we consider the case in which a disruption (random or malicious) can destroy a subset of the arcs, with the cost of the disruption not to exceed a disruption budget. This problem takes the form of a tri-level, two-player game, in which the network operator designs (or augments) the network, then the attacker launches a disruption that destroys a subset of arcs, and then the network operator attempts to find a feasible flow over the residual network. We first show how this can be modeled as a two-stage stochastic program from the network operator's perspective, with each of the exponential number of potential attacks considered as a disruption scenario. We then reformulate this problem, via a Benders decomposition, to consider the recourse decisions implicitly, greatly reducing the number of variables but at the expense of an exponential increase in the number of constraints. We next develop a cut-generation based algorithm. Rather than \emph{explicitly} considering each disruption scenario to identify these Benders cuts, however, we develop a bi-level program and corresponding separation algorithm that enables us to \emph{implicitly} evaluate the exponential set of disruption scenarios. Our computational results demonstrate the efficacy of this approach

Generic Platform for Failure Recovery in Survivable Trees

Failure recovery is a fundamental task of the dependable systems needed to achieve fault-tolerant communications, smooth operation of system components and a comfortable user interface. Tree topologies are fragile, yet they are quite popular structures in computer systems. The term survivable tree denotes the capability of the tree network to deliver messages even in the presence of failures. In this paper, we analyze the characteristics of large-scale overlay survivable trees and identify the requirements for general-purpose failure recovery mechanisms in such an environment. We outline a generic failure recovery platform for preplanned tree restoration which meets those requirements, and we focus primarily on its completeness and correctness properties. The platform is based on bypass rings and it uses a bypass routing algorithm to ensure completeness, and specialized leader election to guarantee correctness. The platform supports multiple, on-line and on-the-fly recovery, provides an optional level of fault-tolerance, protection selectivity and optimization capability. It is independent of the the protected tree type (regarding traffic direction, number of sources, etc.) and forms a basis for application-specific fragment reconnection.

Layered graph approaches for combinatorial optimization problems

Extending the concept of time-space networks, layered graphs associate information about one or multiple resource state values with nodes and arcs. While integer programming formulations based on them allow to model complex problems comparably easy, their large size makes them hard to solve for non-trivial instances. We detail and classify layered graph modeling techniques that have been used in the (recent) scientific literature and review methods to successfully solve the resulting large-scale, extended formulations. Modeling guidelines and important observations concerning the solution of layered graph formulations by decomposition methods are given together with several future research directions

Fault-Tolerant Shortest Paths - Beyond the Uniform Failure Model

The overwhelming majority of survivable (fault-tolerant) network design models assume a uniform scenario set. Such a scenario set assumes that every subset of the network resources (edges or vertices) of a given cardinality $k$ comprises a scenario. While this approach yields problems with clean combinatorial structure and good algorithms, it often fails to capture the true nature of the scenario set coming from applications. One natural refinement of the uniform model is obtained by partitioning the set of resources into faulty and secure resources. The scenario set contains every subset of at most $k$ faulty resources. This work studies the Fault-Tolerant Path (FTP) problem, the counterpart of the Shortest Path problem in this failure model. We present complexity results alongside exact and approximation algorithms for FTP. We emphasize the vast increase in the complexity of the problem with respect to its uniform analogue, the Edge-Disjoint Paths problem

On a generalization of iterated and randomized rounding

We give a general method for rounding linear programs that combines the commonly used iterated rounding and randomized rounding techniques. In particular, we show that whenever iterated rounding can be applied to a problem with some slack, there is a randomized procedure that returns an integral solution that satisfies the guarantees of iterated rounding and also has concentration properties. We use this to give new results for several classic problems where iterated rounding has been useful

Performance Analysis and Design of Mobile Ad-Hoc Networks

We focus on the performance analysis and design of a wireless ad-hoc network using a virtual-circuit or reservation based medium access layer. In a reservation based MAC network, source nodes reserve a session's link capacity end-to-end over the entire path before sending traffic over the established path. An example of a generic reservation based MAC protocol is Unifying Slot Assignment Protocol (USAP). Any reservation based medium access protocol (including USAP) uses a simple set of rules to determine the cells or timeslots available at a node to reserve link capacity along the path to the next node. Given inputs of node locations, traffic pattern between nodes and link propagation matrices, we develop models to estimate blocking probability and throughput for reservation based wireless ad-hoc networks. These models are based on extending reduced load loss network models for a wireless network. For generic USAP with multiple frequency channels, the key effect of multiuser interference on a link is modeled via reduced available link capacity where the effects of transmissions and receptions in the link neighborhood are modeled using USAP reservation rules. We compare our results with simulation and obtain good results using our extended reduced load loss network models but with reduced available link capacity distribution obtained by simulation. For the case of generic USAP using a single frequency channel, we develop models for unicast traffic using reduced load loss network models but with the sharing of the wireless medium between a node and its neighbors modeled by considering cliques of neighboring interfering links around a particular link. We compare results of this model with simulation and show good match. We also develop models to calculate source-destination throughput for the reservation MAC as used in the Joint Tactical Radio System to support both unicast and multicast traffic. These models are based on extending reduced load loss network models for wireless multicast traffic with the sharing of the wireless medium between a node and its (upto 2 hop) neighbors modeled by considering cliques of interfering nodes around a particular node. We compare results of this model with simulation and show good match with simulation. Once we have developed models to estimate throughput and blocking probabilities, we use these models to optimize total network throughput. In order to optimize total throughput, we compute throughput sensitivities of the reduced load loss network model using an implied cost formulation and use these sensitivities to choose the routing probabilities among multiple paths so that total network throughput is maximized. In any network scenario, MANETs can get disconnected into clusters. As part of the MANET design problem, we look at the problem of establishing network connectivity and satisfying required traffic capacity between disconnected clusters by placing a minimum number of advantaged high flying Aerial Platforms (APs) as relay nodes at appropriate places. We also extend the connectivity solution in order to make the network single AP survivable. The problem of providing both connectivity and required capacity between disconnected ground clusters (which contain nodes that can communicate directly with each other) is formulated as a summation-form clustering problem of the ground clusters with the APs along with inter-AP distance constraints that make the AP network connected and with complexity costs that take care of ground cluster to AP capacity constraints. The resultant clustering problem is solved using Deterministic Annealing to find (near) globally optimal solutions for the minimum number and locations of the APs to establish connectivity and provide required traffic capacity between disconnected clusters. The basic connectivity constraints are extended to include conditions that make the resultant network survivable to a single AP failure. In order to make the network single AP survivable, we extend the basic connectivity solution by adding another summation form constraint so that the AP network forms a biconnected network and also by making sure that each ground cluster is connected to atleast two APs. We establish the validity of our algorithms by comparing them with optimal exhaustive search algorithms and show that our algorithms are near-optimal for the problem of establishing connectivity between disconnected clusters