# Branch-and-reduce exponential/FPT algorithms in practice: A case study of vertex cover

@article{Akiba2016BranchandreduceEA, title={Branch-and-reduce exponential/FPT algorithms in practice: A case study of vertex cover}, author={Takuya Akiba and Yoichi Iwata}, journal={Theor. Comput. Sci.}, year={2016}, volume={609}, pages={211-225} }

## 109 Citations

### Exactly Solving the Maximum Weight Independent Set Problem on Large Real-World Graphs

- Computer ScienceALENEX
- 2019

This work develops a full suite of new reductions for the maximum weight independent set problem and provides extensive experiments to show their effectiveness in practice on real-world graphs of up to millions of vertices and edges and shows that combining kernelization with local search produces higher-quality solutions than local search alone.

### Targeted Branching for the Maximum Independent Set Problem

- Computer ScienceSEA
- 2021

This work develops and evaluates several novel branching strategies for both branch- andbound and branch-and-reduce algorithms, which aim to decompose the graph into two or more connected components which can then be solved independently.

### 0/1/All CSPs, Half-Integral A-Path Packing, and Linear-Time FPT Algorithms

- Computer Science, Mathematics2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
- 2018

This paper provides an O(km)-time algorithm for solving the LPs arising from various FPT problems, where k is the optimal value and m is the number of edges/constraints, and obtains linear-time FPT algorithms for various problems.

### A refined algorithm for maximum independent set in degree-4 graphs

- Computer Science, MathematicsJ. Comb. Optim.
- 2017

An upper bound is derived on the time complexity of a polynomial-space algorithm that solves the maximum independent set problem in an n-vertex graph with degree bounded by 4, improving all previous upper bounds on theTime complexity of exact algorithms to this problem.

### Search-Space Reduction via Essential Vertices

- Mathematics, Computer ScienceESA
- 2022

It is shown that under mild conditions a polynomial-time preprocessing algorithm can find a subset of an optimal solution that contains all 2-essential vertices, by exploiting packing/covering duality.

### An Improved-time Polynomial-space Exact Algorithm for TSP in Degree-5 Graphs

- Computer ScienceJ. Inf. Process.
- 2017

A polynomial-space branching algorithm for the TSP in an n-vertex graph with degree at most 5 is presented, and it is shown that it has a running time of O∗(2.3500n), which improves the previous best known time bound of O ∗( 2.4723n) given by the authors.

### Computing a Near-Maximum Independent Set in Dynamic Graphs

- Computer Science2019 IEEE 35th International Conference on Data Engineering (ICDE)
- 2019

This paper proposes a novel scheme, i.e., dependency graph based independent set computation, which can support computing the high-quality independent set on the basis of the previous result rather than calculating from scratch.

### Improved Branching Strategies for Maximum Independent Sets

- Mathematics
- 2020

The NP-complete graph problem maximum independent set is that of finding a set of pairwise non adjacent vertices of largest cardinality [14]. Applications of this problem span multiple real-world…

### Computing A Near-Maximum Independent Set in Linear Time by Reducing-Peeling

- Computer ScienceSIGMOD Conference
- 2017

A Reducing-Peeling framework which iteratively reduces the graph size by applying reduction rules on vertices with very low degrees and temporarily removing the vertex with the highest degree if the reduction rules cannot be applied, and a linear-time algorithm and a near-linear time algorithm that can generate a high-quality independent set from a graph in practice.

### Finding Near-Optimal Weight Independent Sets at Scale

- Computer Science
- 2022

This paper develops an advanced memetic algorithm, which incorporates recent data reduction techniques to compute near-optimal weighted independent sets in huge sparse networks and computes the best results among all competing algorithms for 33 out of 35 instances.

## References

SHOWING 1-10 OF 26 REFERENCES

### A measure & conquer approach for the analysis of exact algorithms

- Computer ScienceJACM
- 2009

The idea is that a smarter measure may capture behaviors of the algorithm that a standard measure might not be able to exploit, and hence lead to a significantly better worst-case time analysis, in order to step beyond limitations of current algorithms design.

### A Faster Algorithm for Dominating Set Analyzed by the Potential Method

- Computer ScienceIPEC
- 2011

This paper extends the measure and conquer analysis and introduces a new analyzing technique named "potential method" to deal with consecutive branchings together and obtained the current fastest algorithm that runs in O(1.4864n) time and polynomial space.

### Half-integrality, LP-branching and FPT Algorithms

- Computer Science, MathematicsSODA
- 2014

A much broader class of half-integral polytopes with the required properties is provided, and a range of new and improved FPT algorithms are yielded, including an O*(|Σ|2k)-time algorithm for node-deletion Unique Label Cover with label set Σ and an O- time algorithm for Group Feedback Vertex Set, including the setting where the group is only given by oracle access.

### Linear-Time FPT Algorithms via Network Flow

- Computer Science, MathematicsSODA
- 2014

This paper gives FPT algorithms with small f(k) and d for many important problems including Odd Cycle Transversal and Almost 2-SAT, and achieves linear time complexity for the first time for these problems.

### A Simple and Faster Branch-and-Bound Algorithm for Finding a Maximum Clique

- Computer ScienceWALCOM
- 2010

This paper proposes new approximate coloring and other related techniques which markedly improve the run time of the branch-and-bound algorithm MCR, previously shown to be the fastest maximum-clique-finding algorithm for a large number of graphs.

### Faster Parameterized Algorithms Using Linear Programming

- Computer Science, MathematicsACM Trans. Algorithms
- 2014

It is argued that combining previously known preprocessing rules with the most straightforward branching algorithm yields an O*(2.618k) algorithm for the problem, and a kernel is obtained for the standard parameterization of Vertex Cover with at most 2k − clog k vertices, simpler than previously known kernels achieving the same size bound.

### Confining sets and avoiding bottleneck cases: A simple maximum independent set algorithm in degree-3 graphs

- Computer Science, MathematicsTheor. Comput. Sci.
- 2013

### A Fine-grained Analysis of a Simple Independent Set Algorithm

- Computer ScienceFSTTCS
- 2009

It is demonstrated how a very simple algo- rithm can outperform more complicated ones if the right analysis of its running time is performed.

### Fast Algorithms for max independent set

- Computer Science, MathematicsAlgorithmica
- 2010

This work proposes a method that “propagates” improvement of the worst-case complexity for “sparse” instances to “denser” ones and shows an easy though non-trivial application of it to the min set cover problem.