Subgraph Isomorphism on Graph Classes that Exclude a Substructure

Bodlaender, Hans L.; Hanaka, Tesshu; Kobayashi, Yasuaki; Kobayashi, Yusuke; Okamoto, Yoshio; Otachi, Yota; Zanden, Tom C. van der

doi:10.1007/s00453-020-00737-z

Cited by 9 publications

(3 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While our TDG model is more restrictive from the point of view that it does not allow agents to derive utilities from nodes in the topology graph, it is more general in that an agent's utility depends not only on neighboring agents on the topology graph, but also on agents further away. Elkind et al (2020) investigated a similar model as Massand and Simon (2019) from the truthfulness perspective, while Bodlaender et al (2020) considered the special case where an agent's utility depends on her neighbors but not on her assigned node.…”

Section: Related Workmentioning

confidence: 99%

Topological Distance Games

Bullinger

Suksompong

2023

AAAI

View full text Add to dashboard Cite

We introduce a class of strategic games in which agents are assigned to nodes of a topology graph and the utility of an agent depends on both the agent's inherent utilities for other agents as well as her distance from these agents on the topology graph. This model of topological distance games (TDGs) offers an appealing combination of important aspects of several prominent settings in coalition formation, including (additively separable) hedonic games, social distance games, and Schelling games. We study the existence and complexity of stable outcomes in TDGs—for instance, while a jump stable assignment may not exist in general, we show that the existence is guaranteed in several special cases. We also investigate the dynamics induced by performing beneficial jumps.

show abstract

Section: Related Workmentioning

confidence: 99%

Topological Distance Games

Bullinger

Suksompong

2023

AAAI

View full text Add to dashboard Cite

show abstract

“…Moreover, it is NP-complete if G is proper interval, trivially perfect, split, and bipartite permutation [31]. When G is disconnected, it is also NP-complete even if G is a forest and a cluster graph whose components are of size three [25,5]. Here, if G is in some graph class G in Spanning Subgraph Isomorphism, we call the problem Spanning Subgraph Isomorphism of G. Then we give the following theorems.…”

Section: 𝐵 𝐵 𝐵mentioning

confidence: 99%

Hedonic Seat Arrangement Problems

Bodlaender,

Hanaka,

Jaffke

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

In this paper, we study a variant of hedonic games, called Seat Arrangement. The model is defined by a bijection from agents with preferences to vertices in a graph. The utility of an agent depends on the neighbors assigned in the graph. More precisely, it is the sum over all neighbors of the preferences that the agent has towards the agent assigned to the neighbor. We first consider the price of stability and fairness for different classes of preferences. In particular, we show that there is an instance such that the price of fairness (PoF) is unbounded in general. Moreover, we show an upper bound d(G) and an almost tight lower bound d(G) − 1/4 of PoF, where d(G) is the average degree of an input graph. Then we investigate the computational complexity of problems to find certain "good" seat arrangements, say Maximum Welfare Arrangement, Maximin Utility Arrangement, Stable Arrangement, and Envy-free Arrangement. We give dichotomies of computational complexity of four Seat Arrangement problems from the perspective of the maximum order of connected components in an input graph. For the parameterized complexity, Maximum Welfare Arrangement can be solved in time n O(γ) , while it cannot be solved in time f (γ) o(γ) under ETH, where γ is the vertex cover number of an input graph. Moreover, we show that Maximin Utility Arrangement and Envy-free Arrangement are weakly NP-hard even on graphs of bounded vertex cover number. Finally, we prove that determining whether a stable arrangement can be obtained from a given arrangement by k swaps is W[1]-hard when parameterized by k + γ, whereas it can be solved in time n O(k) .

show abstract

“…Apart from L(p, 1)-Labeling, twin cover number is a relatively new graph parameter, which is introduced in [20] as a stronger parameter than vertex cover number. In the same paper, many problems are shown to be FPT when parameterized by twin cover number, and it is getting to be a standard parameter (e.g., [1,4,12,21,29,31]). Recently, for Imbalance, which is one of graph layout problems, a parameterized algorithm is presented [34].…”

Section: Related Workmentioning

confidence: 99%

Computing $L(p,1)$-Labeling with Combined Parameters

Hanaka¹,

Kawai²,

Ono³

2020

Preprint

Self Cite

View full text Add to dashboard Cite

Given a graph, an L(p, 1)-labeling of the graph is an assignment f from the vertex set to the set of nonnegative integers such that for any pair of vertices (u, v), |f (u) − f (v)| ≥ p if u and v are adjacent, and f (u) = f (v) if u and v are at distance 2. The L(p, 1)-labeling problem is to minimize the span of f (i.e.,maxu∈V (f (u)) − minu∈V (f (u)) + 1). It is known to be NP-hard even for graphs of maximum degree 3 or graphs with tree-width 2, whereas it is fixedparameter tractable with respect to vertex cover number. Since vertex cover number is a kind of the strongest parameter, there is a large gap between tractability and intractability from the viewpoint of parameterization. To fill up the gap, in this paper, we propose new fixed-parameter algorithms for L(p, 1)-Labeling by the twin cover number plus the maximum clique size and by the tree-width plus the maximum degree. These algorithms reduce the gap in terms of several combinations of parameters.

show abstract

Subgraph Isomorphism on Graph Classes that Exclude a Substructure

Cited by 9 publications

References 32 publications

Topological Distance Games

Topological Distance Games

Hedonic Seat Arrangement Problems

Computing $L(p,1)$-Labeling with Combined Parameters

Contact Info

Product

Resources

About