Worst-Case Analysis of Network Design Problem Heuristics

The Optimal Network problem (as defined by Scott [16]) consists of selecting a subset of arcs that minimizes the sum of the shortest paths between all nodes subject to a budget constraint. This paper considers the worst-case behavior of heuristics for this prob'em. Let n be the number of nodes in the network and e be a constant between 0 and 1. For a general class of Optimal Network Problems, we show that the question of finding a solution which is always less than n times the optimal solution is NP-complete. This indicates that all polynomial-time heuristics for the problem most probably have poor worst-case performance. An upper bound for worst-case heuristic performance of 2n times the optimal solution is also derived. For a restricted version of the Optimal Network problem we describe a procedure whose maximum percentage of error is bounded by a constant.This research was supported, in part, by the U. S. Department of Transportation under Contract DOT-TSC-1058, Transportation Advanced Research Program (TARP)

Heuristics, LPs, and Trees on Trees: Network Design Analyses

We study a class of models, known as overlay optimization problems, with a "base" subproblem and an "overlay" subproblem, linked by the requirement that the overlay solution be contained in the base solution. In some telecommunication settings, a feasible base solution is a spanning tree and the overlay solution is an embedded Steiner tree (or an embedded path). For the general overlay optimization problem, we describe a heuristic solution procedure that selects the better of two feasible solutions obtained by independently solving the base and overlay subproblems, and establish worst-case performance guarantees on both this heuristic and a LP relaxation of the model. These guarantees depend upon worst-case bounds for the heuristics and LP relaxations of the unlinked base and overlay problems. Under certain assumptions about the cost structure and the optimality of the subproblem solutions, both the heuristic and the LP relaxation of the combined overlay optimization model have performance guarantees of 4/3. We extend this analysis to multiple overlays on the same base solution, producing the first known worst-case bounds (approximately proportional to the square root of the number of commodities) for the uncapacitated multicommodity network design problem. In a companion paper, we develop heuristic performance guarantees for various new multi-tier. survivable network design models that incorporate both multiple facility types or technologies and differential node connectivity levels

Task mapping and routing optimization for hard real-time Networks-on-Chip

Interference from high priority tasks and messages in a hard real-time Networks-on-Chip (NoC) create computation and communication delays. As the delays increase in number, maintaining the system’s schedulability become difficult. In order to overcome the problem, one way is to reduce interference in the NoC by changing task mapping and network routing. Some population-based heuristics evaluate the worst-case response times of tasks and messages based on the schedulability analysis, but requires a significant amount of optimization time to complete due to the complexity of the evaluation function. In this paper, we propose an optimization technique that explore both parameters simultaneously with the aim to meet the schedulability of the system, hence reducing the optimization time. One of the advantages from our approach is the unrepeated call to the evaluation function, which is unaddressed in the heuristics that configure design parameters in stages. The results show that a schedulable configuration can be found from the large design space

Doubling or Splitting: Strategies for Modeling and Analyzing Survivable Network Design Problems

Survivability is becoming an increasingly important criterion in network design. This paper studies formulations, heuristic worst-case performance, and linear programming relaxations for two classes of survivable network design problems: the low connectivity Steiner (LCS) problem for graphs containing nodes with connectivity requirement of 0, 1, or 2, and a more general multi-connected network with branches (MNB) that requires connectivities of two or more for certain (critical) nodes and single connectivity for other secondary nodes. We consider both unitary and nonunitary MNB problems that respectively require a connected design or permit multiple components. Using a doubling argument, we first show how to generalize heuristic bounds of the Steiner tree and traveling salesman problems to LCS problems. We then develop a disaggregate formulation for the MNB problem that uses fractional edge selection variables to split the total connectivity requirement across each critical cutset into two separate requirements. This model, which is tighter than the usual cutset formulation, has three special cases: a "secondary-peeling" version that peels off the lowest connectivity level, a "connectivity-dividing" version that divides the connectivity requirements for all the critical cutsets, and a "secondarycompletion" version that attempts to separate the design decisions for the multi-connected network from those for the branches. We examine the tightness of the linear programming relaxations for these extended formulations, and then use them to analyze heuristics for the LCS and MNB problems. Our analysis strengthens some previously known heuristic-to-IP worst-case performance ratios for LCS and MNB problems by showing that the same bounds apply to the heuristic-to-LP ratios using our stronger formulations

Heuristics with Performance Guarantees for the Minimum Number of Matches Problem in Heat Recovery Network Design

Heat exchanger network synthesis exploits excess heat by integrating process hot and cold streams and improves energy efficiency by reducing utility usage. Determining provably good solutions to the minimum number of matches is a bottleneck of designing a heat recovery network using the sequential method. This subproblem is an NP-hard mixed-integer linear program exhibiting combinatorial explosion in the possible hot and cold stream configurations. We explore this challenging optimization problem from a graph theoretic perspective and correlate it with other special optimization problems such as cost flow network and packing problems. In the case of a single temperature interval, we develop a new optimization formulation without problematic big-M parameters. We develop heuristic methods with performance guarantees using three approaches: (i) relaxation rounding, (ii) water filling, and (iii) greedy packing. Numerical results from a collection of 51 instances substantiate the strength of the methods

Measuring and Understanding Throughput of Network Topologies

High throughput is of particular interest in data center and HPC networks. Although myriad network topologies have been proposed, a broad head-to-head comparison across topologies and across traffic patterns is absent, and the right way to compare worst-case throughput performance is a subtle problem. In this paper, we develop a framework to benchmark the throughput of network topologies, using a two-pronged approach. First, we study performance on a variety of synthetic and experimentally-measured traffic matrices (TMs). Second, we show how to measure worst-case throughput by generating a near-worst-case TM for any given topology. We apply the framework to study the performance of these TMs in a wide range of network topologies, revealing insights into the performance of topologies with scaling, robustness of performance across TMs, and the effect of scattered workload placement. Our evaluation code is freely available

The Simulation Model Partitioning Problem: an Adaptive Solution Based on Self-Clustering (Extended Version)

This paper is about partitioning in parallel and distributed simulation. That means decomposing the simulation model into a numberof components and to properly allocate them on the execution units. An adaptive solution based on self-clustering, that considers both communication reduction and computational load-balancing, is proposed. The implementation of the proposed mechanism is tested using a simulation model that is challenging both in terms of structure and dynamicity. Various configurations of the simulation model and the execution environment have been considered. The obtained performance results are analyzed using a reference cost model. The results demonstrate that the proposed approach is promising and that it can reduce the simulation execution time in both parallel and distributed architectures

Cautious Weight Tuning for Link State Routing Protocols

Link state routing protocols are widely used for intradomain routing in the Internet. These protocols are simple to administer and automatically update paths between sources and destinations when the topology changes. However, finding link weights that optimize network performance for a given traffic scenario is computationally hard. The situation is even more complex when the traffic is uncertain or time-varying. We present an efficient heuristic for finding link settings that give uniformly good performance also under large changes in the traffic. The heuristic combines efficient search techniques with a novel objective function. The objective function combines network performance with a cost of deviating from desirable features of robust link weight settings. Furthermore, we discuss why link weight optimization is insensitive to errors in estimated traffic data from link load measurements. We assess performance of our method using traffic data from an operational IP backbone