We study the i.i.d. online bipartite matching problem, a dynamic version of the classical model where one side of the bipartition is fixed and known in advance, while nodes from the other side appear one at a time as i.i.d. realizations of an underlying distribution, and must immediately be matched or discarded. We consider time-indexed relaxations of the set of achievable matching probabilitie...

Let (G,C) be an (edge-)colored bipartite graph with bipartition (X, Y ) and |X| = |Y | = n. A heterochromatic matching of G is such a matching in which no two edges have the same color. Let N c(S) denote a maximum color neighborhood of S ⊆ V (G). In a previous paper, we showed that if N c(S) ≥ |S| for all S ⊆ X or S ⊆ Y , then G has a heterochromatic matching with cardinality at least d3n−1 8 e...

The class of k-ary n-cubes represents the most commonly used interconnection topology for distributed-memory parallel systems. Given an even k P 4, let (V1,V2) be the bipartition of the k-ary 2-cube, fv1, fv2 be the numbers of faulty vertices in V1 and V2, respectively, and fe be the number of faulty edges. In this paper, we prove that there exists a cycle of length k 2max{fv1, fv2} in the k-ar...

In this paper, we propose a honeycomb mesh variation, called a spider web network. Assume that m and n are positive even integers with mP 4. A spider web network SWðm; nÞ is a 3-regular bipartite planar graph with bipartition C and D. We prove that the honeycomb rectangular mesh HREMðm; nÞ is a spanning subgraph of SWðm; nÞ. We also prove that SWðm; nÞ e is hamiltonian for any e 2 E and SWðm; n...

We present an algorithm for the 2-clustering problem with cluster size constraints in the plane assuming `1-norm, that works in O(n logn) time and O(n) space. Such a procedure also solves a full version of the problem, computing the optimal solutions for all possible constraints on cluster sizes. The algorithm is based on a separation result concerning the clusters of any optimal solution of th...

Let (G,C) be an edge-colored bipartite graph with bipartition (X,Y ). A heterochromatic matching of G is such a matching in which no two edges have the same color. Let N c(S) denote a maximum color neighborhood of S ⊆ V (G). We show that if |N c(S)| ≥ |S| for all S ⊆ X, then G has a heterochromatic matching with cardinality at least d |X| 3 e. We also obtain that if |X| = |Y | = n and |N c(S)| ...

The average entanglement entropy (EE) of the energy eigenstates in non-vanishing partitions has been recently proposed as a diagnostic integrability quantum many-body systems. For it to be faithful characterization integrability, should distinguish systems with well-defined classical limit same way unequivocal criteria. We examine class collective spin models characterized by permutation symmet...

We study the i.i.d. online bipartite matching problem, a dynamic version of the classical model where one side of the bipartition is fixed and known in advance, while nodes from the other side appear one at a time as i.i.d. realizations of a uniform distribution, and must immediately be matched or discarded. We consider various relaxations of the polyhedral set of achievable matching probabilit...

We extend the work of Letchford (2000) by introducing a new class of valid inequalities for the traveling salesman problem, called the generalized domino-parity (GDP) constraints. Just as Letchford’s domino-parity constraints generalize comb inequalities, GDP constraints generalize the most well-known multiple-handle constraints, including clique-tree, bipartition, path, and star inequalities. ...