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We present linear-time algorithms for partitioning a path or a tree with weights on the vertices by removing $k$ edges to maximize the minimum-weight component. We also use the same framework to partition a path with weight on the vertices,…
Many real discrete optimization problems (DOPs) are $NP$-hard and contain a huge number of variables and/or constraints that make the models intractable for currently available solvers. Large DOPs can be solved due to their special tructure…
In a bounded max-coloring of a vertex/edge weighted graph, each color class is of cardinality at most $b$ and of weight equal to the weight of the heaviest vertex/edge in this class. The bounded max-vertex/edge-coloring problems ask for…
Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal…
We present an algorithm that enumerates all the minimal triangulations of a graph in incremental polynomial time. Consequently, we get an algorithm for enumerating all the proper tree decompositions, in incremental polynomial time, where…
Finding a maximum-weight matching is a classical and well-studied problem in computer science, solvable in cubic time in general graphs. We consider the specialization called assignment problem where the input is a bipartite graph, and…
Construction of phylogenetic trees and networks for extant species from their characters represents one of the key problems in phylogenomics. While solution to this problem is not always uniquely defined and there exist multiple methods for…
We analyze combinatorial optimization problems over a pair of random point sets of equal cardinal. Typical examples include the matching of minimal length, the traveling salesperson tour constrained to alternate between points of each set,…
Finding a maximum-cardinality or maximum-weight matching in (edge-weighted) undirected graphs is among the most prominent problems of algorithmic graph theory. For $n$-vertex and $m$-edge graphs, the best known algorithms run in…
Finding an optimal assignment between two sets of objects is a fundamental problem arising in many applications, including the matching of `bag-of-words' representations in natural language processing and computer vision. Solving the…
We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…
We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…
I will present a way to implement graph algorithms which is different from traditional methods. This work was motivated by the belief that some ideas from software engineering should be applied to graph algorithms. Re-usability of software…
The fusion of independently obtained stochastic maps by collaborating mobile agents is considered. The proposed approach includes two parts: matching of stochastic maps and maximum likelihood alignment. In particular, an affine invariant…
Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment,…
Constructing the maximum spanning tree $T$ of an edge-weighted connected graph $G$ is one of the important research topics in computer science and optimization, and the related research results have played an active role in practical…
In this paper, we study three algorithmic problems involving computation trees: the optimization, solvability, and satisfiability problems. The solvability problem is concerned with recognizing computation trees that solve problems. The…
Consensus maximization is widely used for robust fitting in computer vision. However, solving it exactly, i.e., finding the globally optimal solution, is intractable. A* tree search, which has been shown to be fixed-parameter tractable, is…
An algorithm is proposed for constructing directed spanning forests of the minimum weight, in which the maximum possible degree of affinity between the minimum forests is preserved when the number of trees changes. The correctness of the…
We determine the maximum distance between any two of the center, centroid, and subtree core among trees with a given order. Corresponding results are obtained for trees with given maximum degree and also for trees with given diameter. The…