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Abstract-This work 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-programmingbased 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.

Many combinatorial optimization problems in the embedded systems and design automation domains involve decision making in multi-dimensional spaces. The multi-dimensional multiple-choice knapsack problem (MMKP) is among the most challenging of the encountered optimization problems. MMKP problem instances appear for example in chip multiprocessor run-time resource management and in global routing of wiring in circuits. Chip multiprocessor resource management requires solving MMKP under real-time constraints, whereas global routing requires scalability of the solution approach to extremely large MMKP instances. This paper presents a novel MMKP heuristic, CPH (for Compositional Pareto-algebraic Heuristic), which is a parameterized compositional heuristic based on the principles of Pareto algebra. Compositionality allows incremental computation of solutions. The parameterization allows tuning of the heuristic to the problem at hand. These aspects make CPH a very versatile heuristic. When tuning CPH for computation time, MMKP instances can be solved in real time with better results than the fastest MMKP heuristic so far. When tuning CPH for solution quality, it finds several new solutions for standard benchmarks that are not found by any existing heuristic. CPH furthermore scales to extremely large problem instances. We illustrate and evaluate the use of CPH in both chip multiprocessor resource management and in global routing.

[13,5,2,4,10]

The main challenge in post-silicon debug is the lack of observability to the internal signals of a chip. Trace buffer technology provides one venue to address this challenge by online tracing of a few selected state elements. Due to the limited bandwidth of the trace buffer, only a few state elements can be selected for tracing. Recent research has focused on automated trace signal selection problem in order to maximize restoration of the untraced state elements using the few traced signals. Existing techniques can be categorized into high quality but slow "simulation-based", and lower quality but much faster "metric-based" techniques. This work presents a new trace signal selection technique which has comparable or better quality than simulation-based while it has a fast runtime, comparable to the metric-based techniques.