Prior work on abiogenesis, the emergence of life from non-life, suggests that it requires chemical reaction networks that contain self-amplifying motifs, namely, autocatalytic cores. However, little is known about how the presence of multiple autocatalytic cores might allow for the gradual accretion of complexity on the path to life. To explore this problem, we develop the concept of a seed-dependent autocatalytic system (SDAS), which is a subnetwork that can autocatalytically self-maintain given a flux of food, but cannot be initiated by food alone. Rather, initiation of SDASs requires the transient introduction of chemical "seeds." We show that, depending on the topological relationship of SDASs in a chemical reaction network, a food-driven system can accrete complexity in a historically contingent manner, governed by rare seeding events. We develop new algorithms for detecting and analyzing SDASs in chemical reaction databases and describe parallels between multi-SDAS networks and biological ecosystems. Applying our algorithms to both an abiotic reaction network and a biochemical one, each driven by a set of simple food chemicals, we detect SDASs that are organized as trophic tiers, of which the higher tier can be seeded by relatively simple chemicals if the lower tier is already activated. This indicates that sequential activation of trophically organized SDASs by seed chemicals that are not much more complex than what already exist could be a mechanism of gradual complexification from relatively simple abiotic reactions to more complex life-like systems. Interestingly, in both reaction networks, higher-tier SDASs include chemicals that might alter emergent features of chemical systems and could serve as early targets of selection. Our analysis provides computational tools for analyzing very large chemical/biochemical reaction networks and suggests new approaches to studying abiogenesis in the lab.

Program coverage is used across many stages of software development. While common during testing, program coverage has also found use outside the test lab, in production software. However, production software has stricter requirements on run-time overheads, and may limit possible program instrumentation. Thus, optimizing the placement of probes to gather program coverage is important.

Local nets are a major contributing factor to mismatch between the global routing (GR) and detailed routing (DR) stages. A local net has all its terminals inside one global cell (gcell) and is traditionally ignored during global routing. This work offers two contributions in order to estimate and manage the local nets at the GR stage. First, a procedure is given to generate gcells of non-uniform size in order to reduce the number of local nets and thus the cumulative error associated with ignoring or approximating them. Second, we approximate the resource usage of local nets at the GR stage by introducing a capacity for each gcell in the GR graph. With these two complementary approaches, we offer a mathematical model for the congestion-aware GR problem that captures local congestion with non-uniform gcells along with other complicating factors of modern designs including variable wire sizes, routing blockages, and virtual pins. A practical routing procedure is presented based on the mathematical model that can solve large industry instances. This procedure is integrated with the CGRIP congestion analysis tool. In the experiments, we evaluate our techniques in planning for local nets during GR while accounting for other sources of congestion using the ISPD11 benchmarks.

This work presents a method for global routing (GR) to minimize interconnect power. We consider design with multi-supply voltage, where level converters are added to nets that connect driver cells to sink cells of higher supply voltage. The level converters are modeled as additional terminals during GR. Given an initial GR solution obtained with the objective of minimizing wirelength, we propose a GR method to detour nets to further save the interconnect power. When detouring routes via this procedure, overflow is not increased, and the increase in wirelength is bounded. The power saving opportunities include: 1) reducing the area capacitance of the routes by detouring from the higher metal layers to the lower ones, 2) reducing the coupling capacitance between adjacent routes by distributing the congestion, and 3) considering different power-weights for each segment of a routed net with level converters (to capture its corresponding supply voltage and activity factor). We present a mathematical formulation to capture these power saving opportunities and solve it using integer programming techniques. In our simulations, we show considerable saving in an interconnect power metric for GR, without any wirelength degradation.

This work presents a fast and flexible framework for congestion analysis at the global routing stage. It captures various factors that contribute to congestion in modern designs. The framework is a practical realization of a proposed parameterized integer programming formulation. The formulation minimizes overflow inside a set of regions covering the layout which is defined by an input resolution parameter. A resolution lower than the global routing grid-graph creates regions that are larger in size than the global-cells. The maximum resolution case simplifies the formulation to minimizing the total overflow which has been traditionally used as a metric to evaluate routability. A novel contribution of this work is to demonstrate that for a small analysis time budget, regional minimization of overflow with a lower resolution allows a more accurate identification of the routing congestion hotspot locations, compared to minimizing the total overflow. It allows generating a more accurate congestion heatmap. The other contributions include several new ideas for a practical realization of the formulation for industry-sized benchmark instances some of which are also improvements to existing global routing procedures. This work also describes coalesCgrip, a simpler variation of our framework which was used to evaluate the ISPD 2011 contest.

This paper introduces GRIP, a global routing technique via integer programming. GRIP optimizes wirelength and via cost directly without going through a traditional layer assignment phase. Candidate routes spanning all the metal layers are generated using a linear programming pricing phase that formally accounts for the impact of existing candidate routes when generating new ones. To make an integer-programming-based approach applicable for today's large-scale global routing instances, the original problem is decomposed into smaller subproblems corresponding to rectangular subregions on the chip together with their net assignments. Route fragments of nets that fall in adjacent subproblems are connected in a flexible manner. In case of overflow, GRIP applies a second-phase optimization that explicitly minimizes overflow. By using integer programming in an effective manner, GRIP obtains high-quality solutions. Specifically, for the ISPD 2007 and 2008 benchmarks, GRIP obtains an average improvement in wirelength and via cost of 9.23% and 5.24%, respectively, when compared to the best result in the open literature.

We propose a parallel global routing algorithm that concurrently processes routing subproblems corresponding to rectangular subregions covering the chip area. The algorithm uses at it core an existing integer programming (IP) formulation---both for routing each subproblem and for connecting them. Concurrent processing of the routing subproblems is desirable for effective parallelization. However, achieving no (or low) overflow global routing solutions without strong, coordinated algorithmic control is difficult. Our algorithm addresses this challenge via a patching phase that uses IP to connect partial routing solutions. Patching provides feedback to each routing subproblem in order to avoid overflow, later when attempting to connect them. The end result is a flexible and highly scalable distributed algorithm for global routing. The method is able to accept as input target runtimes for its various phases and produce high-quality solution within these limits. Computational results show that for a target runtime of 75 minutes, running on a computational grid of few hundred CPUs with 2GB memory, the algorithm generates higher quality solutions than competing methods in the open literature.

We describe a new solver for convex mixed-integer nonlinear programs (MINLPs) that implements a linearization-based algorithm. The solver is based on an algorithm of Quesada and Grossmann [Quesada, I., I. E. Grossmann. 1992. An LP/NLP based branch-and-bound algorithm for convex MINLP optimization problems. Comput. Chemical Engrg. 16(10–11) 937–947] that avoids the complete re-solution of a master mixed-integer linear program (MILP) by adding new linearizations at open nodes of the branch-and-bound tree whenever an integer solution is found. The new solver, FilMINT, combines the MINTO branch-and-cut framework for MILP with filterSQP to solve the nonlinear programs that arise as subproblems in the algorithm. The MINTO framework allows us to easily employ cutting planes, primal heuristics, and other well-known MILP enhancements for MINLPs. We present detailed computational experiments that show the benefit of such advanced MILP techniques. We offer new suggestions for generating and managing linearizations that are shown to be efficient on a wide range of MINLPs. By carefully incorporating and tuning all these enhancements, an effective solver for convex MINLPs is constructed.

We propose GRIP, a scalable global routing technique via Integer Programming (IP). GRIP optimizes wirelength and via cost without going through a layer assignment phase. GRIP selects the route for each net from a set of candidate routes that are generated based on an estimate of congestion generated by a linear programming pricing phase. To achieve scalability, the original IP is decomposed into smaller ones corresponding to balanced rectangular subregions on the chip. We introduce the concept of a floating terminal for a net, which allows flexibility to route long nets going through multiple subregions. We also use the IP to plan the routing of long nets, detouring them from congested subregions. For ISPD 2007 benchmarks, we obtain 3.9% and 11.3% average improvement in wirelength and via cost for the 2D and 3D versions respectively, compared to the best results reported in the open literature.

The football pool problem, which gets its name from a lottery-type game where participants predict the outcome of soccer matches, is to determine the smallest covering code of radius 1 of ternary words of length v. For v = 6, the optimal solution is not known. Using a combination of isomorphism pruning, subcode enumeration, and linear programming-based bounding, running on a high-throughput computational grid consisting of thousands of processors, we are able to improve the lower bound on the size of the optimal code from 65 to 71.

Abstract The network interdiction problem involves interrupting an adversary's ability to maximize flow through a capacitated network by destroying portions of the network. A budget constraint limits the amount of the network that can be destroyed. In this article, we study a stochastic version of the network interdiction problem in which the successful destruction of an arc of the network is a Bernoulli random variable, and the objective is to minimize the maximum expected flow of the adversary. Using duality and linearization techniques, an equivalent deterministic mixed integer program is formulated. The structure of the reformulation allows for the application of decomposition techniques for its solution. Using a parallel algorithm designed to run on a distributed computing platform known as a computational grid, we give computational results showing the efficacy of a sampling‐based approach to solve the problem. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008

We describe a parallel, linear programming and implication-based heuristic for solving set partitioning problems on distributed memory computer architectures. Our implementation is carefully designed to exploit parallelism to greatest advantage in advanced techniques like preprocessing and probing, primal heuristics, and cut generation. A primaldual subproblem simplex method is used for solving the linear programming relaxation, which breaks the linear programming solution process into natural phases from which we can exploit information to find good solutions on the various processors. Implications from the probing operation are shared among the processors. Combining these techniques allows us to obtain solutions to large and difficult problems in a reasonable amount of computing time.

Describes MW (Master-Worker) - a software framework that allows users to quickly and easily parallelize scientific computations using the master-worker paradigm on the Computational Grid. MW provides both a "top-level" interface to application software and a "bottom-level" interface to existing Grid computing toolkits. Both interfaces are briefly described. We conclude with a case study, where the necessary Grid services are provided by the Condor high-throughput computing system, and the MW-enabled application code is used to solve a combinatorial optimization problem of unprecedented complexity.

The branch-and-bound procedure for solving mixed integer programming (MIP) problems using linear programming relaxations has been used with great success for decades. Over the years, a variety of researchers have studied ways of making the basic algorithm more effective. Breakthroughs in the fields of computer hardware, computer software, and mathematics have led to increasing success at solving larger and larger MIP instances. The goal of this article is to survey many of the results regarding branch-and-bound search strategies and evaluate them again in light of the other advances that have taken place over the years. In addition, novel search strategies are presented and shown to often perform better than those currently used in practice.