The steiner tree packing problem in VLSI design

In this paper we describe several versions of the routing problem arising in VLSI design and indicate how the Steiner tree packing problem can be used to model these problems mathematically. We focus on switchbox routing problems and provide integer programming formulations for routing in the knock-knee and in the Manhattan model. We give a brief sketch of cutting plane algorithms that we developed and implemented for these two models. We report on computational experiments using standard test instances. Our codes are able to determine optimum solutions in most cases, and in particular, we can show that some of the instances have no feasible solution if Manhattan routing is used instead of knock-knee routing.     

A generalization of Dijkstra's shortest path algorithm with applications to VLSI routing

We generalize Dijkstra's algorithm for finding shortest paths in digraphs with non-negative integral edge lengths. Instead of labeling individual vertices we label subgraphs which partition the given graph. We can achieve much better running times if the number of involved subgraphs is small compared to the order of the original graph and the shortest path problems restricted to these subgraphs is computationally easy.As an application we consider the VLSI routing problem, where we need to find millions of shortest paths in partial grid graphs with billions of vertices. Here, our algorithm can be applied twice, once in a coarse abstraction (where the labeled subgraphs are rectangles), and once in a detailed model (where the labeled subgraphs are intervals). Using the result of the first algorithm to speed up the second one via goal-oriented techniques leads to considerably reduced running time. We illustrate this with a state-of-the-art routing tool on leading-edge industrial chips.     

Multi-objective evacuation routing in transportation networks

In this paper, the optimal design and analysis of evacuation routes in transportation networks is examined. An methodology for optimal egress route assignment is suggested. An integer programming (IP) formulation for optimal route assignment is presented, which utilizes M/G/c/c state dependent queueing models to cope with congestion and time delays on road links. M/G/c/c simulation software is used to evaluate performance measures of the evacuation plan: clearance time, total travelled distance and blocking probabilities. Extensive experimental results are included.     

An ILP based hierarchical global routing approach for VLSI ASIC design

The use of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been growing at a very fast pace. The level of integration as measured by the number of logic gates in a chip has been steadily rising due to the rapid progress in processing and interconnect technology. The interconnect delay in VLSI circuits has become a critical determiner of circuit performance. As a result, circuit layout is starting to play a more important role in today’s chip designs. Global routing is one of the key sub-problems of circuit layout which involves finding an approximate path for the wires connecting the elements of the circuit without violating resource constraints. In this paper, several integer programming (ILP) based global routing models are fully investigated and explored. The resulting ILP problem is relaxed and solved as a linear programming (LP) problem followed by a rounding heuristic to obtain an integer solution. Experimental results obtained show that the proposed combined WVEM (wirelength, via, edge capacity) model can optimize several global routing objectives simultaneously and effectively. In addition, several hierarchical methods are combined with the proposed flat ILP based global router to reduce the CPU time by about 66% on average for edge capacity model (ECM).     

Routing optimization in packet switching communication networks

For routing assignments a special model and an optimization algorithm are proposed. The efficiency of the routing assignments is evaluated by the average value of the total cost of delays for all packets in the network. It is the objective function. The main idea is that traffic, which is transmitted from the source node to the destination node, can be split between two or more logical paths. The minimum of the objective function can be found by varying the traffic on every path and simultaneously from all the source nodes to the destination nodes. If this approach is applied, then the objective function is nonseparable and nonlinear. Because its shape is unknown in advance, an adaptive nonlinear optimization algorithm is proposed. For evaluating its efficiency a special set of test functions has been used.     

A meta-model for multiobjective routing in MPLS networks

MPLS (Multiprotocol Label Switching) enables the utilisation of explicit routes and other advanced routing mechanisms in multiservice packet networks, capable of dealing with multiple and heterogeneous QoS (Quality of Service) parameters. Firstly the paper presents a discussion of conceptual and methodological issues raised by multiobjective routing optimisation models for MPLS networks. The major contribution is the proposal of a multiobjective routing optimisation framework for MPLS networks. The major features of this modelling framework are: the formulation of a three-level hierarchical routing optimisation problem including network and service performance objectives, the inclusion of fairness objectives in the different levels of optimisation and a two-level stochastic representation of the traffic in the network (traffic flow and packet stream levels). A variant of the general model for two classes of traffic flows, QoS traffic and Best Effort traffic, is also presented. Finally a stochastic teletraffic modelling approach, underlying the optimisation model, is fully described. Work partially supported by programme POSI of the III EC programme cosponsored by FEDER and national funds.     

Cache placement in sensor networks under an update cost constraint

In this paper, we address an optimization problem that arises in the context of cache placement in sensor networks. In particular, we consider the cache placement problem where the goal is to determine a set of nodes in the network to cache/store the given data item, such that the overall communication cost incurred in accessing the item is minimized, under the constraint that the total communication cost in updating the selected caches is less than a given constant. In our network model, there is a single server (containing the original copy of the data item) and multiple client nodes (that wish to access the data item). For various settings of the problem, we design optimal, near-optimal, heuristic-based, and distributed algorithms, and evaluate their performance through simulations on randomly generated sensor networks.     

On minimum congestion routing in rearrangeable multihop lightwave networks

In this article we consider the problem of minimizing the congestion in logically rearrangeable multihop lightwave networks. Namely, we consider a network in which each node is equipped with a small number of transmitters and receivers, and tuning a transmitter at nodei and a receiver at nodej to the same wavelength creates a logical link (i, j) through which traffic could be sent. For a given traffic matrix-the matrix of flows between nodes—the objective is to find the best connectivity diagram and the corresponding flow assignment so that the maximal flow on any link is minimized. We develop a tabu search heuristic that yields a suboptimal connectivity diagram and an optimal flow assignment on it. Computational experiments are conducted on some benchmark data sets, on a real-world traffic matrix, and on some randomly generated problems of larger dimension. The results are compared with known results from the literature and with a known greedy approach. The results suggest that a tabu search—based heuristic is a promising approach for handling this NP-hard combinatorial problem. In addition, we discuss the performance of the method in view of different patterns of input data.     

Energy aware proactive optimized link state routing in mobile ad-hoc networks

In this paper we develop a novel energy aware routing approach for mobile ad hoc network (MANET) problems. The approach is based on using Optimized Link State Routing Protocol. Our Energy Aware OLSR labeled as OLSR_EA measures and predicts per-interval energy consumptions using the well-known Auto-Regressive Integrated Moving Average time series method. We develop a composite energy cost, by considering transmission power consumption and residual energy of each node, and use this composite energy index as the routing metric. Our extensive ns2 simulation experiments show that OLSR_EA substantially prolongs the network lifetime and saves total energy used in MANET. In our experiments we considered different scenarios considering a variety of traffic loads, node mobilities, homogeneous power consumption, and heterogeneous power consumption. Simulation results also confirm that OLSR_EA improves the traffic balance between nodes, and packet delivery ratio in higher node speed. We further develop characteristics of OLSR_EA in power-wise heterogeneous MANET to achieve efficient energy preserving performance.     

Approximations for Steiner Trees with Minimum Number of Steiner Points

Given n terminals in the Euclidean plane and a positive constant, find a Steiner tree interconnecting all terminals with the minimum number of Steiner points such that the Euclidean length of each edge is no more than the given positive constant. This problem is NP-hard with applications in VLSI design, WDM optical networks and wireless communications. In this paper, we show that (a) the Steiner ratio is 1/ 4, that is, the minimum spanning tree yields a polynomial-time approximation with performance ratio exactly 4, (b) there exists a polynomial-time approximation with performance ratio 3, and (c) there exists a polynomial-time approxi-mation scheme under certain conditions.     

Multi-period traffic routing in satellite networks

We introduce a traffic routing problem over an extended planning horizon that appears in geosynchronous satellite networks. Unlike terrestrial (e.g., fiber optic) networks, routing on a satellite network is not transparent to the customers. As a result, a route change is associated with significant monetary penalties that are usually in the form of discounts (up to 40%) offered by the satellite provider to the customer that is affected. The notion of these rerouting penalties requires the network planners to explicitly consider these penalties in their routing decisions over multiple time periods and introduces novel challenges that have not been considered previously in the literature. We develop a branch-and-price-and-cut procedure to solve this problem and describe an algorithm for the associated pricing problem. Our computational work demonstrates that the use of a multi-period optimization procedure as opposed to a myopic period-by-period approach can result in cost reductions up to 13% depending on problem characteristics and network size considered. These cost reductions correspond to potential savings of several hundred million dollars for large satellite providers.     

A cross entropy approach to design of reliable networks

One of the most important parameters determining the performance of communication networks is network reliability. The network reliability strongly depends on not only topological layout of the communication networks but also reliability and availability of the communication facilities. The selection of optimal network topology is an NP-hard problem so that computation time of enumeration-based methods grows exponentially with network size. This paper presents a new solution approach based on cross-entropy method, called NCE, to design of communication networks. The design problem is to find a network topology with minimum cost such that all-terminal reliability is not less than a given level of reliability. To investigate the effectiveness of the proposed NCE, comparisons with other heuristic approaches given in the literature for the design problem are carried out in a three-stage experimental study. Computational results show that NCE is an effective heuristic approach to design of reliable networks.     

Distributed computation of virtual coordinates for greedy routing in sensor networks

Sensor networks are emerging as a paradigm for future computing, but pose a number of challenges in the fields of networking and distributed computation. One challenge is to devise a greedy routing protocol—one that routes messages through the network using only information available at a node or its neighbors. Modeling the connectivity graph of a sensor network as a 3-connected planar graph, we describe how to compute on the network in a distributed and local manner a special geometric embedding of the graph. This embedding supports a geometric routing protocol called “greedy routing” based on the “virtual” coordinates of the nodes derived from the embedding.     

An efficient approximation algorithm for the survivable network design problem

The survivable network design problem (SNDP) is to construct a minimum-cost subgraph satisfying certain given edge-connectivity requirements. The first polynomial-time approximation algorithm was given by Williamson et al. (Combinatorica 15 (1995) 435–454). This paper gives an improved version that is more efficient. Consider a graph ofn vertices and connectivity requirements that are at mostk. Both algorithms find a solution that is within a factor 2k – 1 of optimal fork 2 and a factor 2 of optimal fork = 1. Our algorithm improves the time from O(k ³n⁴) to O ). Our algorithm shares features with those of Williamson et al. (Combinatorica 15 (1995) 435–454) but also differs from it at a high level, necessitating a different analysis of correctness and accuracy; our analysis is based on a combinatorial characterization of the redundant edges. Several other ideas are introduced to gain efficiency. These include a generalization of Padberg and Rao's characterization of minimum odd cuts, use of a representation of all minimum (s, t) cuts in a network, and a new priority queue system. The latter also improves the efficiency of the approximation algorithm of Goemans and Williamson (SIAM Journal on Computing 24 (1995) 296–317) for constrained forest problems such as minimum-weight matching, generalized Steiner trees and others. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.A preliminary version of this paper has appeared in the Proceedings of the Third Mathematical Programming Society Conference on Integer Programming and Combinatorial Optimization, 1993, pp. 57–74.Research supported in part by NSF Grant No. CCR-9215199 and AT & T Bell Laboratories.Research supported in part by Air Force contracts AFOSR-89-0271 and F49620-92-J-0125 and DARPA contracts N00014-89-J-1988 and N00014-92-1799.This research was performed while the author was a graduate student at MIT. Research supported by an NSF Graduate Fellowship, Air Force contract F49620-92-J-0125, DARPA contracts N00014-89-J-1988 and N00014-92-J-1799, and AT & T Bell Laboratories.     

On the communication complexity of Bar-Yehuda, Goldreich and Itai's randomized broadcasting algorithm

The algorithm by Bar-Yehuda, Goldreich and Itai is one of the best known randomized broadcast algorithms for radio networks. Its probability of success and time complexity are nearly optimal. We propose a modification of this algorithm, which decreases the communication complexity, preserving other properties. Moreover, we show that the local communication complexity of the modified algorithm is deterministic.     

Constant memory routing in quasi-planar and quasi-polyhedral graphs

We address the problem of online route discovery for a class of graphs that can be embedded either in two or in three-dimensional space. In two dimensions we propose the class of quasi-planar graphs and in three dimensions the class of quasi-polyhedral graphs. In the former case such graphs are geometrically embedded in R² and have an underlying backbone that is planar with convex faces; however within each face arbitrary edges (with arbitrary crossings) are allowed. In the latter case, these graphs are geometrically embedded in R³ and consist of a backbone of convex polyhedra and arbitrary edges within each polyhedron. In both cases we provide a routing algorithm that guarantees delivery. Our algorithms need only “remember” the source and destination nodes and one (respectively, two) reference nodes used to store information about the underlying face (respectively, polyhedron) currently being traversed. The existence of the backbone is used only in proofs of correctness of the routing algorithm; the particular choice is irrelevant and does not affect the behaviour of the algorithm.     

An optimization-based approach for the design of Bayesian networks

Bayesian networks model conditional dependencies among the domain variables, and provide a way to deduce their interrelationships as well as a method for the classification of new instances. One of the most challenging problems in using Bayesian networks, in the absence of a domain expert who can dictate the model, is inducing the structure of the network from a large, multivariate data set. We propose a new methodology for the design of the structure of a Bayesian network based on concepts of graph theory and nonlinear integer optimization techniques.     

Improved bounds for vehicle routing solutions

We present lower bounds for the vehicle routing problem (VRP) with and without split deliveries, improving the well known bound of Haimovich and Rinnooy Kan. These bounds are then utilized in a design of best-to-date approximation algorithms.     

Perturbation analysis of communication networks with feedback control using stochastic hybrid models

Communication networks may be abstracted through Stochastic Fluid Models (SFM) with the node dynamics described by switched flow equations as various events take place, thus giving rise to hybrid automaton models with stochastic transitions. The inclusion of feedback mechanisms complicates these dynamics. In a tandem setting, a typical feedback mechanism is the control of a node processing rate as a threshold-based function of the downstream node’s buffer level. We consider the problem of controlling the threshold parameters so as to optimize performance metrics involving average workload and packet loss and show how Infinitesimal Perturbation Analysis (IPA) can be used to analyze congestion propagation through a network and develop gradient estimators of such metrics.