Cid C. de Souza

Efficient datapath merging for partially reconfigurable architectures

Reconfigurable systems have been shown to achieve significant performance speedup through architectures that map the most time-consuming application kernel modules or inner loops to a reconfigurable datapath. As each portion of the application starts to execute, the system partially reconfigures the datapath so as to perform the corresponding computation. The reconfigurable datapath should have as few and simple hardware blocks and interconnections as possible, in order to reduce its cost, area, and reconfiguration overhead. To achieve that, hardware blocks and interconnections should be reused as much as possible across the application. We represent each piece of the application as a data-flow graph (DFG). The DFG merging process identifies similarities among the DFGs, and produces a single datapath that can be dynamically reconfigured and has a minimum area cost, when considering both hardware blocks and interconnections. In this paper we present a novel technique for the DFG merge problem, and we evaluate it using programs from the MediaBench benchmark. Our algorithm execution time approaches the fastest previous solution to this problem and produces datapaths with an average area reduction of 20%. When compared to the best known area solution, our approach produces datapaths with area costs equivalent to (and in many cases better than) it, while achieving impressive speedups.

The edge-weighted clique problem: Valid inequalities, facets and polyhedral computations

Abstract Let Kn=(V,E) be the complete undirected graph with weights ce associated to the edges in E. We consider the problem of finding the subclique C=(U,F) of Kn such that the sum of the weights of the edges in F is maximized and |U|⩽b, for some b∈[1,…,n]. This problem is called the Maximum Edge-Weighted Clique Problem (MEWCP) and is NP-hard. In this paper we investigate the facial structure of the polytope associated to the MEWCP introducing new classes of facet defining inequalities. Computational experiments with a branch-and-cut algorithm are reported confirming the strength of these inequalities. All instances with up to 48 nodes could be solved without entering into the branching phase. Moreover, we show that some of these new inequalities also define facets of the Boolean Quadric Polytope and generalize many of the previously known inequalities for this well-studied polytope.

Hybrid Column Generation Approaches for Urban Transit Crew Management Problems

This article considers the overall crew management problem arising from the daily operation of an urban transit bus company that serves the metropolitan area of the city of Belo Horizonte, Brazil. Due to its intrinsic complexity, the problem is divided in two distinct subproblems:crew scheduling andcrew rostering. We have investigated each of these problems using mathematical programming (MP) and constraint logic programming (CLP) approaches. In addition, we developed hybrid column generation algorithms for solving these problems, combining MP and CLP. The hybrid algorithms always performed better, when obtaining optimal solutions, than the two previous isolated approaches. In particular, they proved to be much faster for the scheduling problem. All the proposed algorithms have been implemented and tested over real-world data obtained from the aforementioned company. The coefficient matrix of the linear program associated with some instances of the scheduling problem contains tens of millions of columns; this number is even larger for the rostering problem. The analysis of our experiments indicates that it was possible to find high-quality, and many times optimal, solutions that were suitable for the companys needs. These solutions were obtained within reasonable computational times on a desktop PC.

Scheduling projects with labor constraints

In this paper we consider a labor constrained scheduling problem (LCSP) which is a simplification of a practical problem arising in industry. Jobs are subject to precedence constraints and have specified processing times. Moreover, for each job the labor requirement varies as the job is processed. Given the amount of labor available in each period, the problem is to finish all the jobs as soon as possible, that is, to minimize makespan, subject to the precedence and labor constraints. Several Integer Programming (IP) formulations for this problem are discussed and valid inequalities for these different models are introduced. It turns out that a major drawback in using the IP approach is the weakness of the lower bound relaxations. However, we report computational experiments showing how the solution of the linear relaxation of the IP models can be used to provide good schedules. Solutions arising from these LP-based heuristics are considerably improved by local search procedures. We further exploit the capabilities of local search for LCSP by designing a Tabu Search algorithm. The computational experiments on a benchmark data set show that the Tabu algorithm generates the best known upper bounds for almost all these instances. We also show how IP can be used to provide reasonably good lower bounds for LCSP when the makespan is replaced by suitably modified objective functions. Finally some directions for further investigations which may turn IP techniques into a more interesting tool for solving such a problem are suggested.

The vertex separator problem: a polyhedral investigation

Abstract.The vertex separator (VS) problem in a graph G=(V,E) asks for a partition of V into nonempty subsets A, B, C such that there is no edge between A and B, and |C| is minimized subject to a bound on max{|A|,|B|}. We give a mixed integer programming formulation of the problem and investigate the vertex separator polytope (VSP), the convex hull of incidence vectors of vertex separators. Necessary and sufficient conditions are given for the VSP to be full dimensional. Central to our investigation is the relationship between separators and dominators. Several classes of valid inequalities are investigated, along with the conditions under which they are facet defining for the VSP. Some of our proofs combine in new ways projection with lifting.In a companion paper we develop a branch-and-cut algorithm for the (VS) problem based on the inequalities discussed here, and report on computational experience with a wide variety of (VS) problems drawn from the literature and inspired by various applications.

Vehicle and crew scheduling for urban bus lines

A solution to the urban transportation problem is given by vehicle and crew schedules. These schedules must meet the passenger demand and satisfy technical and contractual restrictions stemming from the daily operation of the lines, while optimizing some measure of operational cost. This work describes a computational tool developed to solve the urban transportation problem in the large metropolitan area of Sao Paulo, Brazil. The techniques used are based on integer programming models coupled with heuristics. The former produces good feasible solutions, and the latter improves the quality of the final solutions. While the operational and labor restrictions are specific to the city of Sao Paulo, the same ideas can inspire similar approaches for solving the urban transportation problem arising in other metropolitan areas.

Constructing nurse schedules at large hospitals

Several heuristics, based on evolutive algorithms and local search, are used to solve the nurse scheduling problem at a large hospital. Due to several intricate and specific restrictions imposed on the schedules, the problem is a difficult one to solve by hand. Moreover, some of the restrictions have a subjective value attached to them, and this constrains the use of exact methods that search for global optima. In order to facilitate the use of the solver modules by the hospital staff, a user interface was also implemented.

A hybrid model for a multiproduct pipeline planning and scheduling problem

Brazilian petrobras is one of the world largest oil companies. Recurrently, it faces a very difficult planning and scheduling problem: how to operate a large pipeline network in order to adequately transport oil derivatives and biofuels from refineries to local markets. In spite of being more economical and environmentally safer, the use of a complex pipeline network poses serious operational difficulties related to resource allocation and temporal constraints. The current approaches known from the literature only consider a few types of constraints and restricted topologies, hence they are far from being applicable to real instances from petrobras. We propose a hybrid framework based on a two-phase problem decomposition strategy. A novel Constraint Programming (CP) model plays a key role in modelling operational constraints that are usually overlooked in literature, but that are essential in order to guarantee viable solutions. The full strategy was implemented and produced very adequate results when tested over large real instances.

Optimal rectangular partitions

Assume that a rectangle R is given on the Euclidean plane together with a finite set P of points that are interior to R. A rectangular partition of R is a partition of the surface of R into smaller rectangles. The length of such a partition equals the sum of the lengths for the line segments that define it. The partition is said to be feasible if no point of P is interior to a partition rectangle. The Rectangular Partitioning Problem (RPP) seeks a feasible rectangular partition of R with the least length. Computational evidence from the literature indicates that RPPs with noncorectilinear points in P, denoted NCRPPs, are the hardest to solve to proven optimality. In this paper, some structural properties of optimal feasible NCRPP partitions are presented. These properties allow substantial reductions in problem input size to be carried out. Additionally, a stronger formulation of the problem is also made possible. Based on these ingredients, a hybrid Lagrangian Relaxation—Linear Programming Relaxation exact solution algorithm is proposed. Such an algorithm has proved capable of solving NCRPP instances more than twice as large as those found in the literature.

The vertex separator problem: algorithms and computations

Abstract.This is a companion paper to our polyhedral study [1] of the Vertex Separator (VS) Problem. Given an undirected graph G, the VS problem consists in identifying a minimum-weight vertex set whose removal disconnects G, subject to bounds on the size of the resulting components. In this paper, we describe versions of a branch-and-cut algorithm based on the results of that polyhedral study. It uses two families of cuts, symmetric and asymmetric, for which we develop polynomial-time greedy separation routines. A heuristic to generate feasible separators is also used. A computational experiment on several data sets from the literature compares the performance of three versions of our algorithm to that of the commercial MIP solver XPRESS. This experiment throws a sharp light on the role of cut density, known to software developers but never before documented in the literature. It convincingly shows that the practical usefulness of cuts in integer programming depends not only on their strength, but also on their sparsity: everything else being equal, the smaller the cut support, the better. The power of the inequalities proposed here is well illustrated by the computational tests on dense graphs. This is in accordance with the previous observation, since the support of these cuts tends to decrease with graph density.