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Topic · Computational Theory and Mathematics

Complexity and Algorithms in Graphs

Complexity and Algorithms in Graphs is a research topic within Computational Theory and Mathematics. Science Explorer counts 21k research works in it since 1959. 9.9% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on combinatorial optimization, approximation algorithms, complexity theory, graph algorithms, submodular functions, network flows, matrix multiplication, communication complexity, linear programming, and algorithmic applications.

  • Combinatorial Optimization
  • Approximation Algorithms
  • Complexity Theory
  • Graph Algorithms
  • Submodular Functions
  • Network Flows
  • Matrix Multiplication
  • Communication Complexity
  • Linear Programming
  • Algorithmic Applications
Research works
21k
fractional, since 1959
In the world top 10%
2.1k
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
-4%
the tick is no change
Largest producer
United States
29% of the 10 largest, 2022-now
Complexity and Algorithms in Graphs

Which countries lead Complexity and Algorithms in Graphs research?

By volume, the United States and China publish the most (756 and 595 works in 2022-now).

By volume, 2022-now

  1. 1 United States 756 works
  2. 2 China 595 works
  3. 3 India 238 works
  4. 4 Germany 236 works
  5. 5 France 176 works
  6. 6 Israel 152 works
  7. 7 Japan 152 works
  8. 8 United Kingdom 140 works
  9. 9 Canada 116 works
  10. 10 Italy 77 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

United States: 28.6%China: 22.5%India: 9.0%Germany: 8.9%6 others listed: 30.8%29%largest
United States756 · 28.6%China595 · 22.5%India238 · 9.0%Germany236 · 8.9%6 others listed815 · 30.8%

Shares of the rows listed above, not of the whole node.

Which institutions lead Complexity and Algorithms in Graphs research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Complexity and Algorithms in Graphs research, followed by Massachusetts Institute of Technology and ETH Zurich.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 71 works
  2. 2 Massachusetts Institute of TechnologyUnited States 41 works
  3. 3 ETH ZurichSwitzerland 39 works
  4. 4 Carnegie Mellon UniversityUnited States 33 works
  5. 5 University of WaterlooCanada 29 works
  6. 6 Tel Aviv UniversityIsrael 28 works
  7. 7 Chinese Academy of SciencesChina 28 works
  8. 8 Helmholtz Association of German Research CentresGermany 25 works
  9. 9 Ben-Gurion University of the NegevIsrael 25 works
  10. 10 Weizmann Institute of ScienceIsrael 22 works

Who are the leading researchers in Complexity and Algorithms in Graphs?

The most-cited researchers publishing on Complexity and Algorithms in Graphs include Li Fei-Fei, Kai You Wang and David H. Haussler.

  1. 1 Li Fei-Fei United States 225k citations
  2. 2 Kai You Wang China 224k citations
  3. 3 David H. Haussler United States 209k citations
  4. 4 Michael I. Jordan United States 182k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Complexity and Algorithms in Graphs?

The most cited paper in Complexity and Algorithms in Graphs is "Public-Key Cryptosystems Based on Composite Degree Residuosity Classes" (Pascal Paillier, 2007), with 7,322 citations. Next come "Identity-Based Encryption from the Weil Pairing" (7,095) and "Fully homomorphic encryption using ideal lattices" (6,742).

Most cited papers
#PaperReleasedCitations
1 Public-Key Cryptosystems Based on Composite Degree Residuosity Classes Pascal Paillier · Lecture notes in computer science Conference paper 10 Oct 2007 7,322
2 Identity-Based Encryption from the Weil Pairing Dan Boneh, Matthew K. Franklin · Lecture notes in computer science Conference paper 2001 7,095
3 Fully homomorphic encryption using ideal lattices Craig Gentry Conference paper 31 May 2009 6,742
4 The Byzantine Generals Problem Leslie Lamport, Robert E. Shostak, Marshall C. Pease · ACM Transactions on Programming Languages and Systems Open access Jul 1982 6,065
5 Combinatorial Optimization: Algorithms and Complexity. David Johnson, Christos H. Papadimitriou, Kenneth Steiglitz · American Mathematical Monthly Mar 1984 6,041
All 97 most cited papers, with filters and sorting

Where is Complexity and Algorithms in Graphs research done?

The largest centres of Complexity and Algorithms in Graphs research in 2022-now are Beijing (China), Paris (France), Tokyo (Japan) and Shanghai (China). Among places with at least 20 works in it, it is an unusually large share of all research in Rehovot, Saarbrücken and Beersheba.

Largest cities, 2022-now

  1. 1 BeijingChina 131 works
  2. 2 ParisFrance 70 works
  3. 3 TokyoJapan 64 works
  4. 4 ShanghaiChina 49 works
  5. 5 New YorkUnited States 45 works
  6. 6 CambridgeUnited States 45 works
  7. 7 ZurichSwitzerland 42 works
  8. 8 ChennaiIndia 40 works
  9. 9 PittsburghUnited States 36 works
  10. 10 HaifaIsrael 33 works

Where it is the local speciality

  1. RehovotIL · 22.2 works42×
  2. SaarbrückenDE · 30.8 works27×
  3. BeershebaIL · 24.8 works19×
  4. HaifaIL · 32.8 works13×
  5. WaterlooCA · 30.5 works13×
  6. Tel AvivIL · 32.3 works12×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Complexity and Algorithms in Graphs than the world average.

See Complexity and Algorithms in Graphs on the map

Where is the best place to study Complexity and Algorithms in Graphs?

Among universities, judged by research, Massachusetts Institute of Technology, Aarhus University and ETH Zurich score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%10%20%30%mean 16.15%fractional works in this field (log) →share of work in the world top 10% →Aarhus UniversityThe University of Te…Massachusetts Instit…ETH Zurich
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Massachusetts Institute of TechnologyUnited States 80.015.5%19.3×41 +2.9%
2Aarhus UniversityDenmark 75.027.1%5.6×15 +24.8%
3ETH ZurichSwitzerland 74.311.3%18.6×39 +11.1%
4The University of Texas at AustinUnited States 61.826.6%6.3×16 -8.4%
5Carnegie Mellon UniversityUnited States 61.211.3%26.5×33 -10.5%
6University of California, BerkeleyUnited States 60.223.3%5.4×16 -35.0%
7École Polytechnique Fédérale de LausanneSwitzerland 59.314.9%12.5×16 +65.7%
8University of WaterlooCanada 57.56.9%17.8×29 +10.8%
9Stanford UniversityUnited States 57.514.9%4.6×20 -38.5%
10Bar-Ilan UniversityIsrael 55.79.7%18.9×16 +11.3%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Complexity and Algorithms in Graphs, country by country

Is Complexity and Algorithms in Graphs research growing?

Output in 2022-2025 was 4% lower than in 2018-2021, peaking in 2015.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Complexity and Algorithms in Graphs as a percentage of every work published that year, 0.011% in 2024.

still counting0.020%0.040%Complexity and Algorithms in Graphs0.014% in 202519801990200020102020

Fractional works of Complexity and Algorithms in Graphs over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Complexity and Algorithms in Graphs9.9% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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