# An Approximation Algorithm for K-best Enumeration of Minimal Connected Edge Dominating Sets with Cardinality Constraints

K-best enumeration, which asks to output k best solutions without duplication, plays an important role in data analysis for many fields. In such fields, data can be typically represented by graphs, and thus subgraph enumeration has been paid much attention to. However, k-best enumeration tends to be intractable since, in many cases, finding one optimum solution is -hard. To overcome this difficulty, we combine k-best enumeration with a new concept of enumeration algorithms called approximation enumeration algorithms, which has been recently proposed. As a main result, we propose an α-approximation algorithm for minimal connected edge dominating sets which outputs k minimal solutions with cardinality at most α· OPT, where OPT is the cardinality of a minimum solution which is not outputted by the algorithm, and α is constant. Moreover, our proposed algorithm runs in O(nm^2Δ) delay, where n, m, Δ are the number of vertices, the number of edges, and the maximum degree of an input graph.

## Authors

• 15 publications
• 17 publications
12/20/2019

### An Õ(log^2 n)-approximation algorithm for 2-edge-connected dominating set

In the Connected Dominating Set problem we are given a graph G=(V,E) and...
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A property Π on a finite set U is monotone if for every X ⊆ U satisfying...
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### Dominating Sets and Connected Dominating Sets in Dynamic Graphs

In this paper we study the dynamic versions of two basic graph problems:...
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### On the maximum number of minimal connected dominating sets in convex bipartite graphs

The enumeration of minimal connected dominating sets is known to be noto...
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### Minimal Dominating Sets in a Tree: Counting, Enumeration, and Extremal Results

A tree with n vertices has at most 95^n/13 minimal dominating sets. The ...
06/26/2019

### Upper and Lower Bounds on Approximating Weighted Mixed Domination

A mixed dominating set of a graph G = (V, E) is a mixed set D of vertice...
12/14/2021

### An algorithm with improved delay for enumerating connected induced subgraphs of a large cardinality

Enumerating all connected induced subgraphs of a given order k is a comp...
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