Related papers: Filling in pattern designs for incomplete pairwise…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies focused on the ways how to express and measure this inconsistency, and several…
Pairwise comparisons between alternatives are a well-known method for measuring preferences of a decision-maker. Since these often do not exhibit consistency, a number of inconsistency indices has been introduced in order to measure the…
We revisit the problem of designing optimal, individually rational matching mechanisms (in a general sense, allowing for cycles in directed graphs), where each player --- who is associated with a subset of vertices --- matches as many of…
Subgraph matching is the problem of finding all the occurrences of a small graph, called the query, in a larger graph, called the target. Although the problem has been widely studied in simple graphs, few solutions have been proposed for…
A geometric graph is a graph whose vertex set is a set of points in the plane and whose edge set contains straight-line segments. A matching in a graph is a subset of edges of the graph with no shared vertices. A matching is called perfect…
We revisit the classical question of the relationship between the diameter of a graph and its expansion properties. One direction is well understood: expander graphs exhibit essentially the lowest possible diameter. We focus on the reverse…
A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent…
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…
We initiate the study of the Diverse Pair of (Maximum/ Perfect) Matchings problems which given a graph $G$ and an integer $k$, ask whether $G$ has two (maximum/perfect) matchings whose symmetric difference is at least $k$. Diverse Pair of…
Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for…
A set of vertices $W$ in a graph $G$ is called resolving if for any two distinct $x,y\in V(G)$, there is $v\in W$ such that ${\rm dist}_G(v,x)\neq{\rm dist}_G(v,y)$, where ${\rm dist}_G(u,v)$ denotes the length of a shortest path between…
We give a procedure that can be used to automatically satisfy invariants of a certain shape. These invariants may be written with the operations intersection, composition and converse over binary relations, and equality over these…
We consider the problem of optimal recovery of true ranking of $n$ items from a randomly chosen subset of their pairwise preferences. It is well known that without any further assumption, one requires a sample size of $\Omega(n^2)$ for the…
The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…
We use computational experiments to find the rectangles of minimum perimeter into which a given number n of non-overlapping congruent circles can be packed. No assumption is made on the shape of the rectangles. In many of the packings…
After the phenomenal success of the PageRank algorithm, many researchers have extended the PageRank approach to ranking graphs with richer structures beside the simple linkage structure. In some scenarios we have to deal with…
This study presents special cases of inconsistent pairwise comparisons PC matrices and analysis of their eigenvalue-based inconsistency index using mathematical methods. All studied special cases of PC matrices are Toeplitz matrices with…
Model-driven software engineering is a suitable method for dealing with the ever-increasing complexity of software development processes. Graphs and graph transformations have proven useful for representing such models and changes to them.…
Incomplete pairwise comparison matrices offer a natural way of expressing preferences in decision making processes. Although ordinal information is crucial, there is a bias in the literature: cardinal models dominate. Ordinal models usually…