The clique-partitioning problem

Bhasker, J.; Samad, Tariq

doi:10.1016/0898-1221(91)90001-k

Cited by 31 publications

(30 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence the choice of the heuristic can be based on the relative priorities of these two measures. Moreover, the computational complexity of MCAT is less than OCAT by a linear factor of the number of vertices in a given graph for solving the clique-partitioning problem [26].…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Reuse-Based Optimization for Prebond and Post-Bond Testing of 3-D-Stacked ICs

Agrawal

Chakrabarty

Widialaksono

2015

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

View full text Add to dashboard Cite

Three-dimensional (3-D) stacking of integrated circuits (ICs) using through-silicon-vias (TSVs) is a promising integration platform for next-generation ICs. Since TSVs are not fully accessible prior to bonding, it is difficult to test the combinational logic between scan flip-flops and TSVs at a prebond stage. In order to increase testability, it has been advocated that wrapper cells (WC) be added at both ends of a TSV. However, a drawback of WC is that they incur area overhead and lead to higher latency and performance degradation on functional paths. Prior work proposed the reuse of scan cells to achieve high testability, thereby reducing the number of WC that need to be inserted; however, practical timing considerations were overlooked and the number of inserted WC was still high. We show that the general problem of minimizing the WC is equivalent to the graph-theoretic minimum clique-partitioning problem, and is therefore NP-hard. We adopt efficient heuristic methods to solve the problem and describe a timing-guided and layoutaware solution. We evaluate the heuristic methods using an exact solution technique based on integer linear programming. We also present design-for-test optimization technique to leverage the reuse-based method during post-bond testing. Results are presented for 3-D-stack implementations of the ITC'99 and the OpenCore benchmark circuits. Index Terms-Automatic test pattern generation (ATPG), design-for-test (Df T), three-dimensional (3-D)-stacked integrated circuit (IC), through-silicon-via (TSV).

show abstract

Section: Resultsmentioning

confidence: 99%

“…We adopt Tseng's algorithm from [25] and method-1 from [26]. We refer to these adaptations as "one-clique-at-a-time" (OCAT) and "multiple-cliques-at-a-time" (MCAT), respectively.…”

Section: Heuristic Methods and Ilp Modelmentioning

confidence: 99%

Reuse-Based Optimization for Prebond and Post-Bond Testing of 3-D-Stacked ICs

Agrawal

Chakrabarty

Widialaksono

2015

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

View full text Add to dashboard Cite

show abstract

“…However, clique partition is a well-known NP-complete problem [23]. Moreover, it can be easily transformed to a graph coloring problem for an inverse graph G inv (V, E inv ), where an edge exists between two vertices v G,k ∈ V and v G,l ∈ V if there is no edge connecting them in G(V, E) [24]. In this work, we color G inv (V, E inv ) using a simple sequential greedy coloring heuristic [25].…”

Section: Graph Coloring Based Approxi-mate Fracturingmentioning

confidence: 99%

Effective model-based mask fracturing for mask cost reduction

Kagalwalla

Gupta

2015

Proceedings of the 52nd Annual Design Automation Conference

View full text Add to dashboard Cite

The use of aggressive resolution enhancement techniques like multiple patterning and inverse lithography (ILT) has led to expensive photomasks. Growing mask write time has been a key reason for the cost increase. Moreover, due to scaling, e-beam proximity effects can no longer be ignored. Model-based mask fracturing has emerged as a useful technique to address these critical challenges by allowing overlapping shots and compensating for proximity effects during fracturing itself. However, it has been shown recently that heuristics for model-based mask fracturing can be suboptimal by more than 1.6× on average for ten real ILT shapes, highlighting the need for better heuristics. In this work, we propose a new model-based mask fracturing method that significantly outperforms all the previously reported heuristics. The number of ebeam shots of our method is 23% less than a state-of-the-art prototype version of capability within a commercial EDA tool for ebeam mask shot decomposition (PROTO-EDA) for ten ILT mask shapes. Moreover, our method has an average runtime of less than 1.4s per shape.

show abstract

“…In order to illustrate how this problem can be solved computationally, the paper will first discuss some important general aspects of sound correspondences and sound correspondence patterns in Section 2, introducing specific terminology that will be needed in the remainder. In Section 3, we will see that the problem of finding sound correspondences across multiple languages can be modeled as the well-known clique-cover problem in an undirected network (Bhasker and Samad, 1991). While this problem is hard to solve in an exact way computationally, 4 fast approximate solutions exist (Welsh and Powell, 1967) and can be easily applied.…”

Section: Introductionmentioning

confidence: 99%

Automatic Inference of Sound Correspondence Patterns Across Multiple Languages

List

2018

Preprint

View full text Add to dashboard Cite

Johann-Mattis List 2018Sound correspondence patterns play a crucial role for linguistic reconstruction. Linguists use them to prove language relationship, to reconstruct proto-forms, and for classical phylogenetic reconstruction based on shared innovations.Cognate words which fail to conform with expected patterns can further point to various kinds of exceptions in sound change, such as analogy or assimilation of frequent words. Here we present an automatic method for the inference of sound correspondence patterns across multiple languages based on a network approach. The core idea is to represent all columns in aligned cognate sets as nodes in a network with edges representing the degree of compatibility between the nodes. The task of inferring all compatible correspondence sets can then be handled as the well-known minimum clique cover problem in graph theory, which essentially seeks to split the graph into the smallest number of cliques in which each node is represented by exactly one clique. The resulting partitions represent all correspondence patterns which can be inferred for a given dataset. By excluding those patterns which occur in only a few cognate sets, the core of regularly recurring sound correspondences can be inferred. Based on this idea, the paper presents a method for automatic correspondence pattern recognition, which is implemented as part of a Python library which supplements the paper. To illustrate the usefulness of the method, we present how the inferred patterns can be used to predict words that have not been observed before.

show abstract

The clique-partitioning problem

Cited by 31 publications

References 6 publications

Reuse-Based Optimization for Prebond and Post-Bond Testing of 3-D-Stacked ICs

Reuse-Based Optimization for Prebond and Post-Bond Testing of 3-D-Stacked ICs

Effective model-based mask fracturing for mask cost reduction

Automatic Inference of Sound Correspondence Patterns Across Multiple Languages

Contact Info

Product

Resources

About