Exploring the Gap Between Treedepth and Vertex Cover Through Vertex Integrity
نویسندگان
چکیده
For intractable problems on graphs of bounded treewidth, two graph parameters treedepth and vertex cover number have been used to obtain fine-grained complexity results. Although the studies in this direction are successful, we still need a systematic way for further investigations because form rather small subclass treedepth. To fill gap, use integrity, which is placed between mentioned above. several problems, generalize fixed-parameter tractability results parameterized by ones integrity. We also show some finer contrasts showing hardness with respect integrity or
منابع مشابه
Treedepth Parameterized by Vertex Cover Number
To solve hard graph problems from the parameterized perspective, structural parameters have commonly been used. In particular, vertex cover number is frequently used in this context. In this paper, we study the problem of computing the treedepth of a given graph G. We show that there are an O(τ(G)3) vertex kernel and an O(4τ(G)τ(G)n) time fixed-parameter algorithm for this problem, where τ(G) i...
متن کاملParameterized Power Vertex Cover
We study a recently introduced generalization of the Vertex Cover (VC) problem, called Power Vertex Cover (PVC). In this problem, each edge of the input graph is supplied with a positive integer demand. A solution is an assignment of (power) values to the vertices, so that for each edge one of its endpoints has value as high as the demand, and the total sum of power values assigned is minimized...
متن کاملVertex Cover Approximations
Often when we talk about an approximation algorithm, we give an approximation ratio. The approximation ratio gives the ratio between our solution and the actual solution. The goal is to obtain an approximation ratio as close to 1 as possible. If the problem involves a minimization, the approximation ratio will be greater than 1; if it involves a maximization, the approximation ratio will be les...
متن کاملReview of Vertex Cover
for a constant c ∈ (1, 2). Using more clever backtracking, one can develop even more complex recurrences and a running time of O(1.27 · poly(n)). For the minimum vertex cover problem, we can therefore solve it on arbitrary graphs in time O∗(1.27n).1 In fact, one can get a slightly better running time for arbitrary graphs, via the following trick. Notice that if the vertex cover is of size at le...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Lecture Notes in Computer Science
سال: 2021
ISSN: ['1611-3349', '0302-9743']
DOI: https://doi.org/10.1007/978-3-030-75242-2_19