Journal ArticleDOI
Algorithmic graph theory and perfect graphs
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This article is published in Order.The article was published on 1986-06-01. It has received 1324 citations till now. The article focuses on the topics: Trivially perfect graph & Perfect graph theorem.read more
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Robust Scheduling of Task Graphs under Execution Time Uncertainty
TL;DR: This work tackles predictable and efficient nonpreemptive scheduling of multitask applications in the presence of duration uncertainty by exploiting a hybrid offline/online technique known as Precedence Constraint Posting (PCP), and the results are very promising, as the PCP schedules exhibit good stability and improved average execution time.
Book ChapterDOI
Treewidth Computation and Extremal Combinatorics
Fedor V. Fomin,Yngve Villanger +1 more
TL;DR: It is proved that every graph on nvertices contains at most $n\binom{b+f}{b}$ such vertex subsets, and this result from extremalcombinatorics appears to be very useful in the design of severalumeration and exact algorithms.
Book ChapterDOI
Colouring Paths in Directed Symmetric Trees with Applications to WDM Routing
TL;DR: It is proved that the minimum number of colours needed to colour the set of all directed paths in T, so that no two paths of the same colour use the sameArc of T, is equal to the maximum number of paths passing through an arc of T.
Posted Content
CS-TSSOS: Correlative and term sparsity for large-scale polynomial optimization
TL;DR: This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solving large-scale sparse polynomial optimization problems, and obtains a two-level hierarchy of semidefinite programming relaxations with the crucial property to involve quasi block-diagonal matrices and the guarantee of convergence to the global optimum.
Journal ArticleDOI
Independent Sets of Maximum Weight in Apple-Free Graphs
TL;DR: This work presents the first polynomial-time algorithm to solve the maximum weight independent set problem for apple-free graphs, which is a common generalization of several important classes where the problem can be solved efficiently.
References
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Journal ArticleDOI
Interval graphs and related topics
TL;DR: A more general paradigm for studying various classes of graphs is suggested which can be described as follows: when 9 is allowed to be an arbitrary family of sets, the class obtained as intersection graphs is all undirected graphs.