The family of judicious partitioning problems, introduced by Bollobás and Scott to the field of extremal combinatorics, has been extensively studied from a structural point of view for over two decades. This rich realm of problems aims to counterbalance the objectives of classical partitioning problems such as Min Cut, Min Bisection and Max Cut. While these classical problems focus solely on th...

A bstract We investigate the ground state of a (1+1)-dimensional conformal field theory (CFT) built with M species massless free Dirac fermions coupled at one boundary point via junction/interface. Each CFT represents wire finite length L . develop systematic strategy to compute Rényi entropies for generic bipartition between wires and entanglement negativity two non-complementary sets wires. B...

In this paper, we show that each f -graph with more than 5 vertices has an unique minimum bipartition, and we also show the upper and lower bound of the balanced size of f -graphs.

This paper addresses the problem of efficient execution of a batch of data-intensive tasks with batch-shared I/O behavior, on coupled storage and compute clusters. Two scheduling schemes are proposed: 1) a 0-1 Integer Programming (IP) based approach, which couples task scheduling and data replication, and 2) a bi-level hypergraph partitioning based heuristic approach (BiPartition), which decoup...

In this paper, we study two fast algorithms—HashRF and PGM-Hashed—for computing the Robinson-Foulds (RF) distance matrix between a collection of evolutionary trees. The RF distance matrix represents a tremendous data-mining opportunity for helping biologists understand the evolutionary relationships depicted among their trees. The novelty of our work results from using a variety of different ar...

A literature search revealed only three case reports of treatment for a symptomatic bipartite medial cuneiform [1,2,5]. Azurza and Sakellarious reported a case of a 34 year old male Soldier with a three year history of symptomatic bipartition following a soccer injury. Successful treatment consisted of arthrodesis [1]. Chiodo and Parentis reported a case of a 32 year old female Olympic marathon...

A bipartition of n is an ordered pair of partitions (λ, μ) such that the sum of all of the parts equals n. In this article, we concentrate on the function c5(n), which counts the number of bipartitions (λ, μ) of n subject to the restriction that each part of μ is divisible by 5. We explicitly establish four Ramanujan type congruences and several infinite families of congruences for c5(n) modulo 3.

It is very well known that every graph on n vertices and m edges admits a bipartition of size at least m/2. This bound can be improved to m/2 + (n − 1)/4 for connected graphs, and m/2 + n/6 for graphs without isolated vertices, as proved by Edwards, and Erdős, Gyárfás, and Kohayakawa, respectively. A bisection of a graph is a bipartition in which the size of the two parts differ by at most 1. W...

In this paper, we consider various problems concerning quasi-matchings and semimatchings in bipartite graphs, which generalize the classical problem of determining a perfect matching in bipartite graphs. We prove a vast generalization of Hall’s marriage theorem, and present an algorithm that solves the problem of determining a lexicographically minimum g-quasi-matching (that is a set F of edges...