Related papers: The Wiener maximum quadratic assignment problem
In the matching interdiction problem, we are given an undirected graph with weights and interdiction costs on the edges and seek to remove a subset of the edges constrained to some budget, such that the weight of a maximum weight matching…
In this paper we consider $m$ ($m \geq 1$)conjunctions of Max-atoms that is atoms of the form $\max(z,y) + r \geq x$, where the offset $r$ is a real constant and $x,y,z$ are variables. We show that the Max-atom problem (MAP) belongs to…
Given two sets of points in the plane, $P$ of $n$ terminals and $S$ of $m$ Steiner points, a Steiner tree of $P$ is a tree spanning all points of $P$ and some (or none or all) points of $S$. A Steiner tree with length of longest edge…
We give polynomial-time approximation schemes for monotone maximization problems expressible in terms of distances (up to a fixed upper bound) and efficiently solvable in graphs of bounded treewidth. These schemes apply in all fractionally…
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…
We study the stable matching problem in non-bipartite graphs with incomplete but strict preference lists, where the edges have weights and the goal is to compute a stable matching of minimum or maximum weight. This problem is known to be…
The paper presents a polynomial time approximation schema for the edge-weighted version of maximum k-vertex cover problem in bipartite graphs.
This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. First, it is…
The maximum intersection problem for a matroid and a greedoid, given by polynomial-time oracles, is shown $NP$-hard by expressing the satisfiability of boolean formulas in 3-conjunctive normal form as such an intersection. The corresponding…
The Wiener index of a connected graph is the sum of topological distances between all pairs of vertices. Since Wang gave a mistake result on the maximum Wiener index for given tree degree sequence, in this paper, we investigate the maximum…
In this paper we initiate the study of the temporal graph realization problem with respect to the fastest path durations among its vertices, while we focus on periodic temporal graphs. Given an $n \times n$ matrix $D$ and a $\Delta \in…
The Wiener polynomial of a connected graph $G$ is defined as $W(G;x)=\sum x^{d(u,v)}$, where $d(u,v)$ denotes the distance between $u$ and $v$, and the sum is taken over all unordered pairs of distinct vertices of $G$. We examine the nature…
The Wiener index of a connected graph is defined as the sum of distances between all its unordered pairs of vertices. Characterising graphs on $n$ vertices with a fixed diameter that maximise the Wiener index is a long-standing open…
We consider new polynomially solvable cases of the well-known Quadratic Assignment Problem involving coefficient matrices with a special diagonal structure. By combining the new special cases with polynomially solvable special cases known…
We consider the problem of finding a subgraph of a given graph which minimizes the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already when all functions are the same, we show that it…
We propose a new exact approach to the generalized graph layering problem that is based on a particular quadratic assignment formulation. It expresses, in a natural way, the associated layout restrictions and several possible objectives,…
In this paper, we solve a maximization problem where the objective function is quadratic and convex or concave and the constraints set is the reachable value set of a convergent discrete-time affine system. Moreover, we assume that the…
For an arbitrary tree we investigate the problems of constructing a maximum matching which minimizes or maximizes the cardinality of a maximum matching of the graph obtained from original one by its removal and present corresponding…
The K-way vertex cut problem} consists in, given a graph G, finding a subset of vertices of a given size, whose removal partitions G into the maximum number of connected components. This problem has many applications in several areas. It…
In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal…