Degree Realization with Minimum Dominating Set

Amotz Bar-Noy; Igor Kalinichev; David Peleg; Dror Rawitz

doi:10.1007/978-3-032-28691-8_5

Degree Realization with Minimum Dominating Set

Amotz Bar-Noy
, Igor Kalinichev
, David Peleg
, Dror Rawitz

Bar-Ilan University - The Alexander Kofkin Faculty of Engineering

City University of New York
Weizmann Institute of Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The Degree Realization problem requires, given a sequence d of n positive integers, to decide whether there exists problems in which the goal is to compute a realization that optimizes some quality measure. Efficient algorithms are known for the problems of finding a realization with the maximum clique, the maximum independent set, or the minimum vertex cover. In this paper, we focus on the Degree Realization with Min Dominating Set problem for which such algorithm was not known. The goal is to find a realization whose minimum dominating set is minimized among all the realizations of the given sequence d. We present polynomial time realization algorithm for this problem. A related problem of interest and importance is characterizing the sequences with a given value of the optimized function. This leads to an efficient computation of the optimized value without providing the realization that achieves that value. This paper provides a succinct characterization of sequences with a dominating set of a given size.

Original language	English
Title of host publication	Integer Programming and Combinatorial Optimization - 27th International Conference, IPCO 2026, Proceedings
Editors	Santanu S. Dey, Marco Di Summa, Domenico Salvagnin
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	64-80
Number of pages	17
ISBN (Print)	9783032286901
DOIs	https://doi.org/10.1007/978-3-032-28691-8_5
State	Published - 2026
Event	27th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2026 - Padua, Italy Duration: 17 Jun 2026 → 19 Jun 2026

Publication series

Name	Lecture Notes in Computer Science
Volume	16588 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	27th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2026
Country/Territory	Italy
City	Padua
Period	17/06/26 → 19/06/26

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.

Keywords

Degree sequences
Graph algorithms
Graph realization

Access to Document

10.1007/978-3-032-28691-8_5

Cite this

Bar-Noy, A., Kalinichev, I., Peleg, D., & Rawitz, D. (2026). Degree Realization with Minimum Dominating Set. In S. S. Dey, M. Di Summa, & D. Salvagnin (Eds.), Integer Programming and Combinatorial Optimization - 27th International Conference, IPCO 2026, Proceedings (pp. 64-80). (Lecture Notes in Computer Science; Vol. 16588 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-032-28691-8_5

Bar-Noy, Amotz ; Kalinichev, Igor ; Peleg, David et al. / Degree Realization with Minimum Dominating Set. Integer Programming and Combinatorial Optimization - 27th International Conference, IPCO 2026, Proceedings. editor / Santanu S. Dey ; Marco Di Summa ; Domenico Salvagnin. Springer Science and Business Media Deutschland GmbH, 2026. pp. 64-80 (Lecture Notes in Computer Science).

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Bar-Noy, A, Kalinichev, I, Peleg, D & Rawitz, D 2026, Degree Realization with Minimum Dominating Set. in SS Dey, M Di Summa & D Salvagnin (eds), Integer Programming and Combinatorial Optimization - 27th International Conference, IPCO 2026, Proceedings. Lecture Notes in Computer Science, vol. 16588 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 64-80, 27th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2026, Padua, Italy, 17/06/26. https://doi.org/10.1007/978-3-032-28691-8_5

Degree Realization with Minimum Dominating Set. / Bar-Noy, Amotz; Kalinichev, Igor; Peleg, David et al.
Integer Programming and Combinatorial Optimization - 27th International Conference, IPCO 2026, Proceedings. ed. / Santanu S. Dey; Marco Di Summa; Domenico Salvagnin. Springer Science and Business Media Deutschland GmbH, 2026. p. 64-80 (Lecture Notes in Computer Science; Vol. 16588 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Bar-Noy A, Kalinichev I, Peleg D, Rawitz D. Degree Realization with Minimum Dominating Set. In Dey SS, Di Summa M, Salvagnin D, editors, Integer Programming and Combinatorial Optimization - 27th International Conference, IPCO 2026, Proceedings. Springer Science and Business Media Deutschland GmbH. 2026. p. 64-80. (Lecture Notes in Computer Science). doi: 10.1007/978-3-032-28691-8_5