Approximation Algorithms for \(\alpha\)-bisubmodular Function Maximization Subject to Matroid Constraint
نویسندگان
چکیده
We design an approximation algorithm for maximizing \(\alpha\)-bisubmodular function with matroid constraint, where the is a generalization of bisubmodular function. The concept \(\alpha\)- bisubmodularity provided by Huber, Krokhin, and Powell [[1], 2014], rank delta-matroids cut capacity directed networks have \(\alpha\)-bisubmodularity. consider two cases problem, monotone non-monotone objective function, respectively. also show that running time ispolynomial.
منابع مشابه
Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
Let f : 2 → R+ be a monotone submodular set function, and let (X, I) be a matroid. We consider the problem maxS∈I f(S). It is known that the greedy algorithm yields a 1/2approximation [14] for this problem. For certain special cases, e.g. max|S|≤k f(S), the greedy algorithm yields a (1− 1/e)-approximation. It is known that this is optimal both in the value oracle model (where the only access to...
متن کاملKnapsack Cover Subject to a Matroid Constraint
We consider the Knapsack Covering problem subject to a matroid constraint. In this problem, we are given an universe U of n items where item i has attributes: a cost c(i) and a size s(i). We also have a demand D. We are also given a matroid M = (U, I) on the set U . A feasible solution S to the problem is one such that (i) the cumulative size of the items chosen is at least D, and (ii) the set ...
متن کاملApproximation Algorithms for Online Weighted Rank Function Maximization under Matroid Constraints
Consider the following online version of the submodular maximization problem under a matroid constraint: We are given a set of elements over which a matroid is defined. The goal is to incrementally choose a subset that remains independent in the matroid over time. At each time, a new weighted rank function of a different matroid (one per time) over the same elements is presented; the algorithm ...
متن کاملFaster approximation algorithms for maximizing a monotone submodular function subject to a b-matching constraint
Maximizing a monotone submodular function subject to a b-matching constraint is increasing in importance due to the application for the content spread maximization problem, but few practical algorithms are known other than the greedy algorithm. The best approximation scheme so far is the local search algorithm, proposed by Feldman, Naor, Schwartz, Ward (2011). It obtains a 1/(2+ 1 k +ε)-approxi...
متن کاملOn Bisubmodular Maximization
Bisubmodularity extends the concept of submodularity to set functions with two arguments. We show how bisubmodular maximization leads to richer value-of-information problems, using examples in sensor placement and feature selection. We present the first constant-factor approximation algorithm for a wide class of bisubmodular maximizations.
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: Journal of advances in mathematics and computer science
سال: 2023
ISSN: ['2456-9968']
DOI: https://doi.org/10.9734/jamcs/2023/v38i31750