Multiplicative auction algorithm for approximate maximum weight bipartite matching
We present an auction algorithm using multiplicative instead of constant weight updates to compute a ( 1 - ε ) -approximate maximum weight matching (MWM) in a bipartite graph with n vertices and m edges in time O ( m ε - 1 ) , beating the running time of the fastest known approximation algorithm of...
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| Published in: | Mathematical programming Vol. 210; no. 1; pp. 881 - 894 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.03.2025
|
| Subjects: | |
| ISSN: | 0025-5610, 1436-4646 |
| Online Access: | Get full text |
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| Summary: | We present an
auction algorithm
using multiplicative instead of constant weight updates to compute a
(
1
-
ε
)
-approximate maximum weight matching (MWM) in a bipartite graph with
n
vertices and
m
edges in time
O
(
m
ε
-
1
)
, beating the running time of the fastest known approximation algorithm of Duan and Pettie [JACM ’14] that runs in
O
(
m
ε
-
1
log
ε
-
1
)
. Our algorithm is very simple and it can be extended to give a dynamic data structure that maintains a
(
1
-
ε
)
-approximate maximum weight matching under (1) one-sided vertex deletions (with incident edges) and (2) one-sided vertex insertions (with incident edges sorted by weight) to the other side. The total time time used is
O
(
m
ε
-
1
)
, where
m
is the sum of the number of initially existing and inserted edges. |
|---|---|
| ISSN: | 0025-5610 1436-4646 |
| DOI: | 10.1007/s10107-024-02066-3 |