Related papers: Theoretical Aspects of Generating Instances with U…
The vertex cover problem is a famous combinatorial problem, and its complexity has been heavily studied. While a 2-approximation can be trivially obtained for it, researchers have not been able to approximate it better than 2-\textit{o}(1).…
We introduce a new technique for designing fixed-parameter algorithms for cut problems, namely randomized contractions. We apply our framework to obtain the first FPT algorithm for the Unique Label Cover problem and new FPT algorithms with…
The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a…
Horiyama et al. (AAAI 2024) studied the problem of generating graph instances that possess a unique minimum vertex cover under specific conditions. Their approach involved pre-assigning certain vertices to be part of the solution or…
An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
The maximum bipartite matching problem is among the most fundamental and well-studied problems in combinatorial optimization. A beautiful and celebrated combinatorial algorithm of Hopcroft and Karp (1973) shows that maximum bipartite…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
Counting the solution number of combinational optimization problems is an important topic in the study of computational complexity, especially on the #P-complete complexity class. In this paper, we first investigate some organizations of…
Recently, there has been increasing interest and progress in improvising the approximation algorithm for well-known NP-Complete problems, particularly the approximation algorithm for the Vertex-Cover problem. Here we have proposed a…
This work introduces two techniques for the design and analysis of branching algorithms, illustrated through the case study of the Vertex Cover problem. First, we present a method for automatically generating branching rules through a…
Combinatorial optimization problems are a prominent application area of evolutionary algorithms, where the (1+1) EA is one of the most investigated. We extend this algorithm by introducing some problem knowledge with a specialized mutation…
Many NP-hard problems, such as Dominating Set, are FPT parameterized by clique-width. For graphs of clique-width $k$ given with a $k$-expression, Dominating Set can be solved in $4^k n^{O(1)}$ time. However, no FPT algorithm is known for…
$H$-Packing is the problem of finding a maximum number of vertex-disjoint copies of $H$ in a given graph $G$. $H$-Partition is the special case of finding a set of vertex-disjoint copies that cover each vertex of $G$ exactly once. Our goal…
Optimization problems consist of either maximizing or minimizing an objective function. Instead of looking for a maximum solution (resp. minimum solution), one can find a minimum maximal solution (resp. maximum minimal solution). Such…
While research in robust optimization has attracted considerable interest over the last decades, its algorithmic development has been hindered by several factors. One of them is a missing set of benchmark instances that make algorithm…
For a collection $\mathcal{F}$ of graphs, the $\mathcal{F}$-\textsc{Contraction} problem takes a graph $G$ and an integer $k$ as input and decides if $G$ can be modified to some graph in $\mathcal{F}$ using at most $k$ edge contractions.…
Our goal in this paper is to propose a \textit{combinatorial algorithm} that beats the only such algorithm known previously, the greedy one. We study the polynomial approximation of the Maximum Vertex Cover Problem in bipartite graphs by a…
Most optimization problems are notoriously hard. Considerable efforts must be spent in obtaining an optimal solution to certain instances that we encounter in the real world scenarios. Often it turns out that input instances get modified…