Abstract
| Original language | English |
|---|---|
| Title of host publication | Approximation and Online Algorithms |
| Editors | Klaus Jansen, Monaldo Mastrolilli |
| Place of Publication | Cham |
| Publisher | Springer International Publishing |
| Pages | 183-196 |
| Number of pages | 14 |
| ISBN (Print) | 978-3-319-51741-4 |
| Publication status | Published - 2017 |
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A priori TSP in the Scenario Model. / van Ee, Martijn; van Iersel, Leo; Janssen, Teun; Sitters, R.A.
Approximation and Online Algorithms. ed. / Klaus Jansen; Monaldo Mastrolilli. Cham : Springer International Publishing, 2017. p. 183-196.Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review
TY - GEN
T1 - A priori TSP in the Scenario Model
AU - van Ee, Martijn
AU - van Iersel, Leo
AU - Janssen, Teun
AU - Sitters, R.A.
PY - 2017
Y1 - 2017
N2 - In this paper, we consider the a priori traveling salesman problem (TSP) in the scenario model. In this problem, we are given a list of subsets of the vertices, called scenarios, along with a probability for each scenario. Given a tour on all vertices, the resulting tour for a given scenario is obtained by restricting the solution to the vertices of the scenario. The goal is to find a tour on all vertices that minimizes the expected length of the resulting restricted tour. We show that this problem is already NP-hard and APX-hard when all scenarios have size four. On the positive side, we show that there exists a constant-factor approximation algorithm in three restricted cases: if the number of scenarios is fixed, if the number of missing vertices per scenario is bounded by a constant, and if the scenarios are nested. Finally, we discuss an elegant relation with an a priori minimum spanning tree problem.
AB - In this paper, we consider the a priori traveling salesman problem (TSP) in the scenario model. In this problem, we are given a list of subsets of the vertices, called scenarios, along with a probability for each scenario. Given a tour on all vertices, the resulting tour for a given scenario is obtained by restricting the solution to the vertices of the scenario. The goal is to find a tour on all vertices that minimizes the expected length of the resulting restricted tour. We show that this problem is already NP-hard and APX-hard when all scenarios have size four. On the positive side, we show that there exists a constant-factor approximation algorithm in three restricted cases: if the number of scenarios is fixed, if the number of missing vertices per scenario is bounded by a constant, and if the scenarios are nested. Finally, we discuss an elegant relation with an a priori minimum spanning tree problem.
M3 - Conference contribution
SN - 978-3-319-51741-4
SP - 183
EP - 196
BT - Approximation and Online Algorithms
A2 - Jansen, Klaus
A2 - Mastrolilli, Monaldo
PB - Springer International Publishing
CY - Cham
ER -