Incremental List Coloring of Graphs, Parameterized by Conservation

Hartung, Sepp; Niedermeier, Rolf

doi:10.1007/978-3-642-13562-0_24

Cited by 5 publications

(5 citation statements)

References 14 publications

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“…There have been a number of papers investigating the complexity of "dynamic problems" in various application domains [19][20][21] , but only one (to the best of our knowledge) that investigates the parameterized complexity of an dynamic problem -the recent pioneering paper of Hartung and Niedermeier [22] that inspired this paper.…”

Section: Almost a Dominating Setmentioning

confidence: 99%

“…The two storylines, as reflected in our two main results, appear to be closely related. We first found the result that DDS is FPT, and then, inspired by the pioneering work of Hartung and Niedermeier [22] (who proved an FPT result for INCREMENTAL LIST COLORING seemingly motivated by the potential application to FPT-turbo-charging a common greedy heuristic for GRAPH COLORING), we then began to look for a greedy heuristic for DOMINATING SET for which our FPT result about DDS could serve as the turbo-charging FPT subroutine, thus in some sense, working backwards to the flow of motivation in Ref. [22].…”

Section: Turbo-charging a Greedy Heuristicmentioning

confidence: 99%

“…Beyond "nothing to lose" we believe that both research directions may be quite practical and profitable -but to determine if this is so will require some serious engagement with algorithms engineering and implementation, such as in Ref. [22].…”

Section: Summary and Research Horizonsmentioning

confidence: 99%

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Dynamic dominating set and turbo-charging greedy heuristics

Downey

Egan

Fellows

et al. 2014

Tinshhua Sci. Technol.

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The main purpose of this paper is to exposit two very different, but very general, motivational schemes in the art of parameterization and a concrete example connecting them. We introduce a dynamic version of the DOMINATING SET problem and prove that it is fixed-parameter tractable (FPT). The problem is motivated by settings where problem instances evolve. It also arises in the quest to improve a natural greedy heuristic for the DOMINATING SET problem.

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Section: Almost a Dominating Setmentioning

confidence: 99%

Section: Turbo-charging a Greedy Heuristicmentioning

confidence: 99%

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Dynamic dominating set and turbo-charging greedy heuristics

Downey

Egan

Fellows

et al. 2014

Tinshhua Sci. Technol.

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“…As to the similarity scenario, one may think of robustness in the sense of "path maintenance": every deviation from the path used before causes additional costs (set up, preparation, checking) and thus shall be kept at a minimum. This can be interpreted in the spirit of incremental changes (evolutionary rather than radical changes) [11,30].…”

Section: Introductionmentioning

confidence: 99%

Multistage s–t Path: Confronting Similarity with Dissimilarity

et al. 2023

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Addressing a quest by Gupta et al. (in: Proceedings of the 41st international colloquium on automata, languages, and programming (ICALP 2014), vol 8572 of LNCS. Springer, pp 563–575, 2014), we provide a first, comprehensive study of finding a short s–t path in the multistage graph model, referred to as the Multistages–tPath problem. Herein, given a sequence of graphs over the same vertex set but changing edge sets, the task is to find short s–t paths in each graph (“snapshot”) such that in the found path sequence the consecutive s–t paths are “similar”. We measure similarity by the size of the symmetric difference of either the vertex set (vertex-similarity) or the edge set (edge-similarity) of any two consecutive paths. We prove that these two variants of Multistages–tPath are already $${\text {NP}}$$ NP -hard for an input sequence of only two snapshots and maximum vertex degree four. Motivated by this fact and natural applications of this scenario e.g. in traffic route planning, we perform a parameterized complexity analysis. Among other results, for both variants, vertex- and edge-similarity, we prove parameterized hardness ($${\text {W[1]}}$$ W[1] -hardness) regarding the parameter path length (solution size). As a further conceptual investigation, we then modify the multistage model by asking for dissimilar consecutive paths. As one of the main technical results (employing so-called representative sets known from non-temporal settings), we prove that dissimilarity allows for fixed-parameter tractability for the parameter solution size, contrasting with our W[1]-hardness proof of the corresponding similarity case. We also provide partially positive results concerning efficient and effective data reduction (kernelization).

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“…Typically, one wants to avoid (if possible) too radical changes in the solution relative to perhaps moderate changes in the input. The corresponding study of incremental algorithms attracted research on numerous problems and scenarios [26], including among many others shortest path computation [43], flow computation [34], clustering problems [10,38], and graph coloring [30].…”

Section: Introductionmentioning

confidence: 99%

Deepening the (Parameterized) Complexity Analysis of Incremental Stable Matching Problems

Boehmer¹,

Heeger²,

Niedermeier³

2022

Preprint

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When computing stable matchings, it is usually assumed that the preferences of the agents in the matching market are fixed. However, in many realistic scenarios, preferences change over time. Consequently, an initially stable matching may become unstable. Then, a natural goal is to find a matching which is stable with respect to the modified preferences and as close as possible to the initial one. For Stable Marriage/Roommates, this problem was formally defined as Incremental Stable Marriage/Roommates by Bredereck et al. [AAAI '20]. As they showed that Incremental Stable Roommates and Incremental Stable Marriage with Ties are NP-hard, we focus on the parameterized complexity of these problems. We answer two open questions of Bredereck et al. [AAAI '20]:We show that Incremental Stable Roommates is W[1]-hard parameterized by the number of changes in the preferences, yet admits an intricate XP-algorithm, and we show that Incremental Stable Marriage with Ties is W[1]-hard parameterized by the number of ties. Furthermore, we analyze the influence of the degree of "similarity" between the agents' preference lists, identifying several polynomial-time solvable and fixed-parameter tractable cases, but also proving that Incremental Stable Roommates and Incremental Stable Marriage with Ties parameterized by the number of different preference lists are W[1]-hard.

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Incremental List Coloring of Graphs, Parameterized by Conservation

Cited by 5 publications

References 14 publications

Dynamic dominating set and turbo-charging greedy heuristics

Dynamic dominating set and turbo-charging greedy heuristics

Multistage s–t Path: Confronting Similarity with Dissimilarity

Deepening the (Parameterized) Complexity Analysis of Incremental Stable Matching Problems

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