What is he best known for?
The fields of study he is best known for:
- Algorithm
- Combinatorics
- Discrete mathematics
His main research concerns Combinatorics, Discrete mathematics, Approximation algorithm, Planar graph and Outerplanar graph.
His biological study spans a wide range of topics, including Node and Algorithm, Combinatorial optimization.
His work on Planar straight-line graph, Book embedding and Polynomial-time approximation scheme as part of general Discrete mathematics study is frequently linked to k-minimum spanning tree, bridging the gap between disciplines.
His Approximation algorithm research integrates issues from Linear programming and Multi-commodity flow problem.
Philip N. Klein focuses mostly in the field of Planar graph, narrowing it down to matters related to 1-planar graph and, in some cases, Treewidth.
The various areas that he examines in his Steiner tree problem study include Network planning and design and Performance guarantee.
His most cited work include:
- Recognition of shapes by editing their shock graphs (666 citations)
- Faster Shortest-Path Algorithms for Planar Graphs (358 citations)
- When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks (355 citations)
What are the main themes of his work throughout his whole career to date?
Philip N. Klein mainly focuses on Combinatorics, Discrete mathematics, Planar graph, Approximation algorithm and Time complexity.
Steiner tree problem, 1-planar graph, Book embedding, Pathwidth and Chordal graph are among the areas of Combinatorics where Philip N. Klein concentrates his study.
His studies deal with areas such as Scheme and Bounded function as well as Discrete mathematics.
His Planar graph study also includes
- Outerplanar graph together with Shortest Path Faster Algorithm,
- Algorithm and related Upper and lower bounds, Floyd–Warshall algorithm and Theoretical computer science.
His Approximation algorithm research is multidisciplinary, incorporating perspectives in Binary logarithm, Class, Multi-commodity flow problem and Graph.
His study in Time complexity is interdisciplinary in nature, drawing from both Vertex, Minimum cut and Constant.
He most often published in these fields:
- Combinatorics (64.83%)
- Discrete mathematics (53.79%)
- Planar graph (39.31%)
What were the highlights of his more recent work (between 2016-2020)?
- Planar graph (39.31%)
- Discrete mathematics (53.79%)
- Combinatorics (64.83%)
In recent papers he was focusing on the following fields of study:
Philip N. Klein mainly investigates Planar graph, Discrete mathematics, Combinatorics, Bounded function and Vehicle routing problem.
Philip N. Klein interconnects Upper and lower bounds, Algorithm, Optimization problem and Graph in the investigation of issues within Planar graph.
His Discrete mathematics study combines topics from a wide range of disciplines, such as Travelling salesman problem and Approximation algorithm.
His Treewidth study in the realm of Combinatorics interacts with subjects such as Redistricting.
His Treewidth study combines topics in areas such as Spanner, Shortest path problem and Steiner tree problem.
His study explores the link between Bounded function and topics such as Time complexity that cross with problems in Embedding and Vertex.
Between 2016 and 2020, his most popular works were:
- Local Search Yields Approximation Schemes for $k$-Means and $k$-Median in Euclidean and Minor-Free Metrics (25 citations)
- Multiple-Source Multiple-Sink Maximum Flow in Directed Planar Graphs in Near-Linear Time (19 citations)
- Polynomial-Time Approximation Schemes for k-center, k-median, and Capacitated Vehicle Routing in Bounded Highway Dimension (15 citations)
In his most recent research, the most cited papers focused on:
- Algorithm
- Combinatorics
- Discrete mathematics
His scientific interests lie mostly in Combinatorics, Planar graph, Additive error, Embedding and Treewidth.
His work blends Combinatorics and Redistricting studies together.
Planar graph is a subfield of Discrete mathematics that Philip N. Klein explores.
Discrete mathematics is closely attributed to Flow network in his study.
His Additive error research incorporates elements of Time complexity, Vertex, Independent set and Metric.
In general Regular polygon, his work in Convex polygon is often linked to Power linking many areas of study.
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