David Shallcross

A polynomial algorithm for a one machine batching problem

A problem of batching identical jobs on a single machine is studied. Constant processing times and batch setup times are assumed. An algorithm is presented to minimize the sum over all jobs of the batched completion times, and shown to run in time polynomial in the logarithms of the problem parameters.

An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming

In recent years many advances have been made in solution techniques for specially structured 0-1 integer programming problems. In contrast, very little progress has been made on solving general (mixed integer) problems. This, of course, is not true when viewed from the theoretical side: Lenstra (1981) made a major breakthrough, obtaining a polynomial-time algorithm when the number of integer variables is fixed. We discuss a practical implementation of a Lenstra-like algorithm, based on the generalized basis reduction method of Lovasz and Scarf (1988).This method allows us to avoid the ellipsoidal approximations required in Lenstras algorithm. We report on the solution of a number of small (but difficult) examples, up to 100 integer variables. Our computer code uses the linear programming optimizer CPlex as a subroutine to solve the linear programming problems that arise.

Distance Realization Problems with Applications to Internet Tomography

In recent years, a variety of graph optimization problems have arisen in which the graphs involved are much too large for the usual algorithms to be effective. In these cases, even though we are not able to examine the entire graph (which may be changing dynamically), we would still like to deduce various properties of it, such as the size of a connected component, the set of neighbors of a subset of vertices, etc. In this paper, we study a class of problems, called distance realization problems, which arise in the study of Internet data traffic models. Suppose we are given a set S of terminal nodes, taken from some (unknown) weighted graph. A basic problem is to reconstruct a weighted graph G including S, with possibly additional vertices, that realizes the given distance matrix for S. We will first show that this problem is not only difficult bu the solution is often unstable in the sense that even if all distances between nodes in S decrease, the solution can increase by a factor proportional to the size of S in the worst case. We then proceed to consider a weaker version of the realization problem that only requires the distances in G to upper bound the given distances. We will show that this weak realization problem is NP-complete and that its optimum solutions can be approximated to within a factor of 2. We also consider several variants of these problems and a number of heuristics are presented. These problems are of interest for monitoring large-scale networks and for supplementing network management techniques.

Network science based approaches to design and analyze MANETs for military applications

Mobile ad hoc networks have become the basis of the militarys network-centric warfare (NCW) approach. However, for NCW to be successful, it is imperative that the networks be designed in a robust manner with the capability to produce consistent predictable results despite the uncertainties of the underlying environment. This underscores the need for formal systematic methodologies to design and predict performance of such networks. The challenges of mobile ad hoc networking combined with those associated with the stringent requirements posed by NCW systems, however, are daunting, and thus no systematic design techniques for NCW system design exist. To address this problem, a joint project was initiated between CERDEC and Telcordia Technologies to develop the Network Engineering Design Analytic Toolset (NEDAT) - a toolset that applies network-science-based approaches to design MANETs for use in NCW. Rooted in formal/analytic techniques, NEDAT can be used to design MANETs for use in NCW given information about available resources and performance objectives, analyze performance of a given NCW network, and understand design trades.

Cognitive tactical network models

Unlike commercial MANET applications, tactical networks are typically hierarchical and involve heterogeneous types of radio communications. Future tactical networks also require cognitive functions across the protocol stack to exploit scarce spectrum and dynamically adapt functions and configuration settings. In this work we highlight the need for novel design tools for cognitive tactical networks. We define a system design model that will provide the foundation for generic network design problem formulations via the use of cognitive techniques covering both dynamic frequency adaptations and machinelearning- related aspects of cognition. We use the system model to identify several potential cognitive design knobs and describe how the different design knobs can potentially be adjusted at different timescales of operation. These knobs are used in formulating a cognitive network design problem. Finally, we discuss how a network designer can potentially benefit from the proposed model result, a cognitive network design toolset we have recently developed.

The Frobenius problem and maximal lattice free bodies

Let p = (p1,…,pn,) be a vector of positive integers whose greatest common divisor is unity. The Frobenius problem is to find the largest integer f* which cannot be written as a nonnegative integral combination of the pi. In this note we relate the Frobenius problem to the topic of maximal lattice free bodies and describe an algorithm for n = 3.

Maximizing the transparency advantage in optical networks

We enhance the potential cost savings from optical network transparency by applying connected dominating sets and impairment-aware routing, thus reducing the density of OEO nodes substantially below that obtained with more straightforward path improvement heuristics. The funding support of NIST ATP contract 70NANB8H4018 is gratefully acknowledged.

Network restoration under a single link or node failure using Preconfigured Virtual Cycles

This paper presents a design algorithm for networks with a restoration mechanism that provides failure-independent, end-to-end path protection to a set of given demands under a single link or node failure with a focus on optical networks. The restoration routes are provided on preconfigured cycles, where each of the demands is assigned a single restoration route and specific restoration wavelengths on a segment of one cycle (splitting is not allowed). The number of reserved restoration wavelengths may vary from one link to the next on a cycle; hence, we refer to these cycles as Preconfigured Virtual Cycles (PVCs). The network design algorithm consists of three major parts. The first part generates a large number of candidate PVCs. Our algorithm allows assignment of certain demands that have common failure scenarios to the same PVC. The second part selects a set of PVCs from among the candidates, attempting to minimize the total reserved restoration cost while ensuring that each demand is assigned to one PVC. This is achieved by solving a set covering problem followed by elimination of duplicate assignments. The third part resolves conflicts of wavelength assignments.

Network restoration under dual failures using path-protecting preconfigured cycles

This paper presents a design algorithm for networks with a restoration mechanism that provides end-to-end path protection to a set of demands with specified working routes, where demands must survive one or two failures in optical networks and these failures may occur almost instantaneously. Each of the demands protected from two failures is assigned two restoration routes and restoration wavelengths on a cycle. A demand protected from a single failure is assigned one restoration route and restoration wavelengths on a cycle. These assignments are preconfigured so that switching and wavelength conversions are not needed at intermediate nodes of restoration routes. Splitting of demand across multiple restoration routes upon a failure occurrence is not allowed. The algorithm generates a large number of candidate Path-Protecting Preconfigured Cycles (PP-PCs). A candidate cycle may provide protection to a mix of demands requiring different protection levels, where demands may share under certain conditions restoration wavelengths even if they are exposed to common failure scenarios and have overlapping restoration routes. A near-optimal set of preconfigured cycles is selected from among all candidates, attempting to minimize the total cost of restoration wavelengths while ensuring that each demand is assigned to a single preconfigured cycle. This is achieved by solving a set covering problem followed by deleting duplicate demand assignments and by resolving wavelength assignment conflicts.

C-NEDAT: A cognitive network engineering design analytic toolset for MANETs

Future force networks of the types envisioned for the network centric warfare (NCW) paradigm will be highly diverse, with the diversity spanning a wide range of (a) requirements (e.g., need for capacity, connectivity, survivability), (b) resources (e.g., radios with widely different capabilities and ‘smart’ (e.g., Software Defined Radios (SDRs)), and (c) environments (e.g., urban, rural). The need to facilitate robust and adaptable communications in such networks has in turn triggered research in the area of cognitive networks that have the ability to ‘learn’ and generate real-time control actions to adapt to the wide diversity of requirements, resources and environments. However, the combination of diversity and “smart” networking exacerbates the problem of generating reliable and robust network designs. We present in this paper, our work on the use of cognitive mechanisms to assist with the design and analysis of robust NCW-like networks. Based on formal network-science based approaches, our Cognitive Network Engineering Design Analytic Toolset (C-NEDAT) provides for a systematic way to design, analyze and maintain robustness of future force MANETs. We provide in this paper an overview of the key functional modules and design capabilities of C-NEDAT and present example results.