@inproceedings{2faf457a6a7b428ba7254a49e6f028a6,
title = "Minimum Sum Vertex Cover: Kernelization and Parameterized Algorithms",
abstract = "Given an ordering of the vertices of a graph, the cost of covering an edge is the smaller number of its two ends. The minimum sum vertex cover problem asks for an ordering that minimizes the total cost of covering all edges. We consider parameterized complexity of this problem, using the largest cost k of covering a single edge as the parameter. Note that the first k vertices form a (not necessarily minimal) vertex cover of the graph, and the ordering of vertices after k is irrelevant. We present a (k2+2k)-vertex kernel and an O(m+2kk!k4)-time algorithm for the minimum sum vertex cover problem, where m is the size of the input graph. Since our parameter k is polynomially bounded by the vertex cover number of the input graph, our results also apply to that parameterization.",
keywords = "Buss reduction, Minimum sum vertex cover, vertex cover",
author = "Jingyi Liu and Yixin Cao and Ling Gai and Jianxin Wang",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.; 30th International Computing and Combinatorics Conference, COCOON 2024 ; Conference date: 23-08-2024 Through 25-08-2024",
year = "2025",
doi = "10.1007/978-981-96-1090-7\_12",
language = "English",
isbn = "9789819610891",
series = "Lecture Notes in Computer Science",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "140--150",
editor = "Yong Chen and Xiaofeng Gao and Xiaoming Sun and An Zhang",
booktitle = "Computing and Combinatorics - 30th International Conference, COCOON 2024, Proceedings",
address = "Germany",
}