Related papers: On Finding Optimal Polytrees
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…
We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the…
It is required to find an optimal order of constructing the edges of a network so as to minimize the sum of the weighted connection times of relevant pairs of vertices. Construction can be performed anytime anywhere in the network, with a…
The branching algorithm is a fundamental technique for designing fast exponential-time algorithms to solve combinatorial optimization problems exactly. It divides the entire solution space into independent search branches using…
A natural way to deal with multiple, partially conflicting objectives is turning all the objectives but one into budget constraints. Some classical polynomial-time optimization problems, such as spanning tree and forest, shortest path,…
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. Some of the most…
A Bayesian network is a directed acyclic graph that represents statistical dependencies between variables of a joint probability distribution. A fundamental task in data science is to learn a Bayesian network from observed data.…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
Dynamic programming over tree decompositions is a common technique in parameterized algorithms. In this paper, we study whether this technique can also be applied to compute Pareto sets of multiobjective optimization problems. We first…
We consider the problems of computing maximal palindromes and distinct palindromes in a trie. A trie is a natural generalization of a string, which can be seen as a single-path tree. There is a linear-time offline algorithm to compute…
The problem of covering minimum cost common bases of two matroids is NP-complete, even if the two matroids coincide, and the costs are all equal to 1. In this paper we show that the following special case is solvable in polynomial time:…
Understanding spatial correlation is vital in many fields including epidemiology and social science. Lee, Meeks and Pettersson (Stat. Comput. 2021) recently demonstrated that improved inference for areal unit count data can be achieved by…
We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one…
We investigate the complexity of finding a transformation from a given spanning tree in a graph to another given spanning tree in the same graph via a sequence of edge flips. The exchange property of the matroid bases immediately yields…
Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis. We introduce a novel and general…
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…
We study the complexity of finding communication trees with the lowest possible completion time for rooted, irregular gather and scatter collective communication operations in fully connected, $k$-ported communication networks under a…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
The collection of all the strongly connected components in a directed graph, among each cluster of which any node has a path to another node, is a typical example of the intertwining structure and dynamics in complex networks, as its…