Faster approximation for maximum independent set on unit disk graph

Nandy, Subhas C.; Pandit, Supantha; Roy, Sasanka

doi:10.1016/j.ipl.2017.07.007

Cited by 10 publications

(5 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to provide a meaningful classical reference benchmark, we reviewed several approximation algorithms [26,27,[30][31][32][33] for UD-MIS and more specifically Polynomial-Time Approximation Schemes (PTAS, see section II B below). Overall, all classical approximation approaches for UD-MIS [25][26][27]33] consist in splitting the input graph into sub-instances that are solved exactly, and returning the union of the sub-solutions as a result.…”

Section: Results Of the Classical Approachmentioning

confidence: 99%

“…The design of this heuristic was motivated by the relative complexity of existing Polynomial-Time Approximation Schemes [26,27,30,32]. While they all consist in splitting a graph into sub-instances that are solved independently, several decompositions generally have to be considered, before making a choice guaranteeing a lower bound on the approximation ratio.…”

Section: A Locality-based Heuristic a Description Of The Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Solving optimization problems with Rydberg analog quantum computers: Realistic requirements for quantum advantage using noisy simulation and classical benchmarks

Serret,

Marchand,

Ayral

2020

Preprint

View full text Add to dashboard Cite

Section: Results Of the Classical Approachmentioning

confidence: 99%

Section: A Locality-based Heuristic a Description Of The Methodsmentioning

confidence: 99%

Solving optimization problems with Rydberg analog quantum computers: Realistic requirements for quantum advantage using noisy simulation and classical benchmarks

Serret,

Marchand,

Ayral

2020

Preprint

View full text Add to dashboard Cite

“…The relation between the Rydberg blockade mechanism and Mis on unit disk graph however suggests intriguing questions related to approximate optimization. Remarkably, polynomial time approximation algorithms exist for Mis on unit disk graphs [38]. It would be interesting to explore if quantum approximate optimization algorithms (QAOA) for the corresponding problems [14] can outperform these classical approximate methods.…”

Section: Discussionmentioning

confidence: 99%

Computational complexity of the Rydberg blockade in two dimensions

Pichler¹,

Wang²,

Zhou³

et al. 2018

Preprint

View full text Add to dashboard Cite

We discuss the computational complexity of finding the ground state of the two-dimensional array of quantum bits that interact via strong van der Waals interactions. Specifically, we focus on systems where the interaction strength between two spins depends only on their relative distance x and decays as 1/x 6 that have been realized with individually trapped homogeneously excited neutral atoms interacting via the so-called Rydberg blockade mechanism. We show that the solution to NP-complete problems can be encoded in ground state of such a many-body system by a proper geometrical arrangement of the atoms. We present a reduction from the NP-complete maximum independent set problem on planar graphs with maximum degree three. Our results demonstrate that computationally hard optimization problems can be naturally addressed with coherent quantum optimizers accessible in near term experiments.

show abstract

“…Recall from Section 1 that OPT(MIS) ≤ OPT(MBS) ≤ 2OPT(MIS). Nandy et al [24] designed a factor-2 approximation algorithm for the MIS problem on unit disks, which runs in O(n 2 ) time. Consequently, we obtain an O(n 2 )-time 4-approximation algorithm for MBS on unit disks.…”

Section: Unit Disks and Unit Squaresmentioning

confidence: 99%

Maximum Bipartite Subgraph of Geometric Intersection Graphs

Jana

Maheshwari

Mehrabi

et al. 2020

WALCOM: Algorithms and Computation

Self Cite

View full text Add to dashboard Cite

We study the Maximum Bipartite Subgraph (MBS) problem, which is defined as follows. Given a set S of n geometric objects in the plane, we want to compute a maximum-size subset S ⊆ S such that the intersection graph of the objects in S is bipartite. We first show that the MBS problem is NP-hard on geometric graphs for which the maximum independent set is NP-hard (hence, it is NP-hard even on unit squares and unit disks). On the algorithmic side, we first give a simple O(n)-time algorithm that solves the MBS problem on a set of n intervals. Then, we give an O(n log n)-time algorithm that computes a near-optimal solution for the problem on circular-arc graphs. Moreover, for the approximability of the problem, we first present a PTAS for the problem on unit squares and unit disks that runs in in O(f (n)n 1/ ) time for any > 0,where f (n) is a computable function that is polynomial in n. Then, we present efficient approximation algorithms with small-constant factors for the problem on unit squares, unit disks and unit-height rectangles. Finally, we study a closely related geometric problem, called Maximum Trianglefree Subgraph (MTFS), where the objective is the same as that of MBS except the intersection graph induced by the set S needs to be trianglefree only (instead of being bipartite).

show abstract

Faster approximation for maximum independent set on unit disk graph

Cited by 10 publications

References 11 publications

Solving optimization problems with Rydberg analog quantum computers: Realistic requirements for quantum advantage using noisy simulation and classical benchmarks

Solving optimization problems with Rydberg analog quantum computers: Realistic requirements for quantum advantage using noisy simulation and classical benchmarks

Computational complexity of the Rydberg blockade in two dimensions

Maximum Bipartite Subgraph of Geometric Intersection Graphs

Contact Info

Product

Resources

About