An improved approximation guarantee for Prize-Collecting TSP Article Swipe
Jannis Blauth
,
Martin Nägele
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2212.03776
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2212.03776
We present a new approximation algorithm for the (metric) prize-collecting traveling salesperson problem (PCTSP). In PCTSP, opposed to the classical traveling salesperson problem (TSP), one may not include a vertex of the input graph in the returned tour at the cost of a given vertex-dependent penalty, and the objective is to balance the length of the tour and the incurred penalties for omitted vertices by minimizing the sum of the two. We present an algorithm that achieves an approximation guarantee of $1.774$ with respect to the natural linear programming relaxation of the problem. This significantly reduces the gap between the approximability of classical TSP and PCTSP, beating the previously best known approximation factor of $1.915$. As a key ingredient of our improvement, we present a refined decomposition technique for solutions of the LP relaxation, and show how to leverage components of that decomposition as building blocks for our tours.
Related Topics
Concepts
Linear programming relaxation
Approximation algorithm
Leverage (statistics)
Travelling salesman problem
Vertex (graph theory)
Mathematics
Relaxation (psychology)
Combinatorics
Decomposition
Mathematical optimization
Linear programming
Metric (unit)
Graph
Computer science
Engineering
Biology
Operations management
Psychology
Social psychology
Ecology
Statistics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2212.03776
- https://arxiv.org/pdf/2212.03776
- OA Status
- green
- Cited By
- 1
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4310926554
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4310926554Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2212.03776Digital Object Identifier
- Title
-
An improved approximation guarantee for Prize-Collecting TSPWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2022Year of publication
- Publication date
-
2022-12-07Full publication date if available
- Authors
-
Jannis Blauth, Martin NägeleList of authors in order
- Landing page
-
https://arxiv.org/abs/2212.03776Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2212.03776Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2212.03776Direct OA link when available
- Concepts
-
Linear programming relaxation, Approximation algorithm, Leverage (statistics), Travelling salesman problem, Vertex (graph theory), Mathematics, Relaxation (psychology), Combinatorics, Decomposition, Mathematical optimization, Linear programming, Metric (unit), Graph, Computer science, Engineering, Biology, Operations management, Psychology, Social psychology, Ecology, StatisticsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1Per-year citation counts (last 5 years)
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.solutions | 129 |
| abstract_inverted_index.technique | 127 |
| abstract_inverted_index.traveling | 10, 20 |
| abstract_inverted_index.components | 139 |
| abstract_inverted_index.ingredient | 118 |
| abstract_inverted_index.minimizing | 65 |
| abstract_inverted_index.previously | 108 |
| abstract_inverted_index.relaxation | 89 |
| abstract_inverted_index.programming | 88 |
| abstract_inverted_index.relaxation, | 133 |
| abstract_inverted_index.salesperson | 11, 21 |
| abstract_inverted_index.improvement, | 121 |
| abstract_inverted_index.approximation | 4, 78, 111 |
| abstract_inverted_index.decomposition | 126, 142 |
| abstract_inverted_index.significantly | 94 |
| abstract_inverted_index.approximability | 100 |
| abstract_inverted_index.prize-collecting | 9 |
| abstract_inverted_index.vertex-dependent | 44 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile |