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Institution

Center for Discrete Mathematics and Theoretical Computer Science

FacilityPiscataway, New Jersey, United States
About: Center for Discrete Mathematics and Theoretical Computer Science is a facility organization based out in Piscataway, New Jersey, United States. It is known for research contribution in the topics: Local search (optimization) & Optimization problem. The organization has 140 authors who have published 175 publications receiving 2345 citations.


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TL;DR: This paper generalizes Opsut's result to the competition numbers of generalized line graphs, that is, it is shown that the competition number of a generalized line graph is at most two, and give necessary conditions and sufficient con ditions for the competitionNumber of a normalized line graph being one.
Abstract: In 1982, Opsut showed that the competition number of a line graph is at most two and gave a necessary and sufficient condition for the competition number of a line graph being one. In this note, we generalize this result to the competition numbers of generalized line graphs, that is, we show that the competition number of a generalized line graph is at most two, and give necessary conditions and sufficient conditions for the competition number of a generalized line graph being one.
Proceedings ArticleDOI
05 Dec 2021
TL;DR: Zhang et al. as mentioned in this paper formulated the centerline extraction problem as a Voronoi diagram to collect centerline points and presented a graph-based invalid centerline removal algorithm to generate an initial centerline result.
Abstract: With the continued feature-size shrinking in modern circuit designs, the layout performance estimation and parasitic import calculation based on the extracted centerline result play an important role in mask verification. Most previous works on layout centerline extraction focus on identifying the connectivity among the devices in a mask layout, with few ones collecting accurate centerline information for mask verification while considering design constraints. In this paper, we first formulate the centerline extraction problem as a Voronoi diagram to collect centerline points. Then, we present a graph-based invalid centerline removal algorithm to generate an initial centerline result. Finally, a complexity-driven centerline optimization method is proposed to further optimize the centerline while considering design constraints. Compared with the commercial 3D-RC parasitic parameter extraction tool RCExplorer and the 1st place in the 2019 EDA Elite Challenge Contest, experimental results show that our algorithm achieves the highest average precision ratio of 99.8% on centerline extraction while satisfying all design constraints in the shortest runtime.
DissertationDOI
13 Jun 2023
TL;DR: In this paper , the authors investigate the verification of dissipativity properties of unknown LTI (linear time invariant) systems using input-output data and the application of the approach to a fault detection method.
Abstract: Dissipativity property is a concept introduced in the early 70s by Jan C. Willems, to describe the input-output behaviour of a dissipative system. The main idea of this concept follows the energy conservation laws, where the rate change of a system's energy function, called storage function, is upper bounded by the power or work done to the system, commonly referred to as the supply-rate function. We call the inequality that describe this behavior as dissipativity inequality. As most real-world applications belong to the class of dissipative systems, investigating theoretical methods to analyse and deal with such systems can be the base of many practical solutions, for instance fault detection. In this thesis, we specifically investigate the verification of dissipativity properties of unknown LTI (linear time invariant) systems using input-output data and the application of the approach to a fault detection method. For validating our theoretical results, we apply the proposed methods in numerical simulations and practical real-world applications. The first practical application concerns to an educational two-degree-of-freedom planar manipulator from Quanser. Using data obtained from experiments using this manipulator, we are able to verify the dissipativity and subsequently apply the proposed fault detection algorithm and observe its advantages when comparing it to a standard principal component analysis algorithm. The second main practical study case is an ultra-high vacuum chemical vapor deposition (UHVCVD) process.
DissertationDOI
02 Jun 2023
TL;DR: In this paper , the authors studied the problem of finding sparsest cuts of a graph and showed that the problem can be solved in polynomial time for a number of graph classes such as claw-free graphs, co-graphs, outerplanar graphs and graph classes with bounded treewidth.
Abstract: In this thesis, three different graph concepts are studied. A graph $(V,E)$ consists of a set of vertices $V$ and a set of edges $E$. Graphs are often used as a model for telecommunication networks, where the nodes of the network are represented by the vertices, and an edge is present between two vertices if the corresponding nodes are joined by a direct connection in the network. The two vertices joined by an edge are called its end vertices, and these two vertices are neighbors of each other. The degree of a vertex is its number of neighbors. The problems in this thesis can be explained and motivated using applications in the area of network design and analysis, which is done in Chapter 1. This chapter also contains the basic definitions that will be used. The first problem we study is the problem of finding sparsest cuts of a graph. For a non-empty proper subset of the vertices $S \subset V$ ,$[S,\overline{S}]$ denotes the set of edges with one end vertex in $S$, which is an \emph{edge cut}. An edge cut $[S \overline{S}]$ is a sparsest cut if its density ${|[S,\overline{S}]| \over |S||\overline{S}|}$ is minimum, over all edge cuts of the graph. Sparsest cuts are closely related to all-to-all flows in networks, and we also discuss an application related to network reliability. In general, the problem of finding sparsest cuts or calculating their density is ${\cal NP}$-hard. However, for three classes of well-structured graphs we characterize the sparsest cuts in Chapter 2. These classes are Cartesian product graphs, unit interval graphs and complete bipartite graphs. Secondly, matching-cuts are studied. A matching is a set of edges that pairwise have no end vertices in common, and a matching-cut is an edge cut that is also a matching. The problem of deciding whether a graph admits a matching-cut is ${\cal NP}$-complete. In Chapter 3 we show that the problem remains ${\cal NP}$-complete when restricted to planar graphs with maximum degree four. We show that the problem can be decided in polynomial time for a number of graph classes such as claw-free graphs, co-graphs, outerplanar graphs, and graph classes with bounded treewidth in general. In Chapter 4, graphs without a matching-cut are studied, which are called (matching) immune. Farley and Proskurowski proved that for all immune graphs on $n$ vertices with $m$ edges, $m \ge \lceil 3(n-1)/2\rceil$, and constructed a large class of immune graphs attaining this lower bound for every value of $n$, called $ABC$ graphs. In Chapter 4, we prove their conjecture that all matching immune graphs with $m = \lceil 3(n-1)/2\rceil$ are $ABC$ graphs. The third topic of this thesis is spanning trees with many leaves. A spanning tree of a graph is a connected subgraph that contains all vertices, with a minimum number of edges. A leaf of a spanning tree is a vertex with degree one. Finding spanning trees with many leaves is another problem that often occurs in network design. In Chapter 5 we show that connected graphs on $n$ vertices, without triangles, with minimum degree at least three, have a spanning tree with at least $(n+4)/3$ leaves. In addition we present a more general but weaker result; we show that connected graphs on $n$ vertices, with minimum degree at least three, have a spanning tree with at least $(2n-D+12)/7$ leaves, where $D$ is the number of diamonds in the graph induced by degree three vertices (a diamond is a $K_4$ minus an edge). Both results are best possible and constructive. In Chapter 6 we give an algorithm for deciding whether a graph on $n$ vertices has a spanning tree with at least $k$ leaves, using the second result from Chapter 5. This problem is ${\cal NP}$-complete. The complexity of the algorithm is $g(n)+ f(k)$, where $g(n)$ is a polynomial and $f(k) \in O(8.12^k)$. It follows that this is a Fixed Parameter Tractable (FPT) algorithm, when $k$ is viewed as the parameter of the problem. This is the current fastest FPT algorithm for this problem.

Authors

Showing all 148 results

NameH-indexPapersCitations
Aravind Srinivasan6026613711
Ding-Zhu Du5242113489
Elena N. Naumova472328593
Rebecca N. Wright371134722
Boris Mirkin351786722
Mona Singh32915451
Fred S. Roberts321815286
Tanya Y. Berger-Wolf311353624
Rephael Wenger26671900
Marios Mavronicolas261512880
Seoung Bum Kim261652260
M. Montaz Ali261013093
Lazaros K. Gallos24694770
Myong K. Jeong24951955
Nina H. Fefferman231072362
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Performance
Metrics
No. of papers from the Institution in previous years
YearPapers
20233
20226
202112
202017
20198
201822