While every instance of the Hospitals/Residents problem admits a stable matching, the problem with lower quotas (HR-LQ) has instances with no stable matching. For such an instance, we expect the existence of an envy-free matching, which is a relaxation of a stable matching preserving a kind of fairness property. In this paper, we investigate the existence of an envy-free matching in several set...

First-order term unification is an essential concept in areas like functional and logic programming, automated deduction, deductive databases, artificial intelligence, information retrieval, compiler design, etc. We build upon recent developments in grammar-based compression mechanisms for terms and investigate algorithms for first-order unification and matching on compressed terms. We prove th...

Several sequences of graphs are introduced whose perfect matching numbers, or Kekulé numbers, K(G), are either Fibonacci or Lucas numbers, or their multiples. Since the ratio of the K(G)s of consecutive members converges to the golden ratio, these sequences of graphs belong to another class of golden family graphs.

In this paper, we revisit the Property Matching problem studied by Amir et al. [Property Matching and Weighted Matching, CPM 2006] and present a better indexing scheme for the problem. In particular, the data structure by Amir et al., namely PST, requires O(n log |Σ|+ n log log n) construction time and O(m log |Σ|+ K) query time, where n and m are the length of, respectively, the text and the p...

The amount of information that we are dealing with today is being generated at an everincreasing rate. On one hand, data compression is needed to efficiently store, organize the data and transport the data over the limited-bandwidth network. On the other hand, efficient information retrieval is needed to speedily find the relevant information from this huge mass of data using available resource...

Permutation Pattern Matching (or PPM) is a decision problem whose input is a pair of permutations π and τ , represented as sequences of integers, and the task is to determine whether τ contains a subsequence order-isomorphic to π. Bose, Buss and Lubiw proved that PPM is NP-complete on general inputs. We show that PPM is NP-complete even when π has no decreasing subsequence of length 3 and τ has...

e∈F x(e). M denotes the set of all perfect matchings of G. χ denotes the incidence vector of M . Cuts: A cut of G is a subset of E that is the coboundary ∂(S) of some subset S of V . For a cut C := ∂(S), S and S are the shores of C. A cut is trivial if one of its shores is a singleton. A cut is odd if both its shores have odd cardinality. Note: This is the notation used in Bondy and Murty’s boo...

For a graph property P, we define a P-matching as a set M of disjoint edges such that the subgraph induced by the vertices incident to M has property P. Previous examples include strong/induced matchings and uniquely restricted matchings. We explore the general properties of P-matchings, but especially the cases where P is the property of being acyclic or the property of being disconnected. We ...

In this paper, we study the relations between the numerical structure of the optimal solutions of a convex programming problem defined on the edge set of a simple graph and the stability number (i.e. the maximum size of a subset of pairwise non-adjacent vertices) of the graph. Our analysis shows that the stability number of every graph G can be decomposed in the sum of the stability number of a...