We study the problem of counting the number of popular matchings in a given instance. McDermid and Irving gave a poly-time algorithm for counting the number of popular matchings when the preference lists are strictly ordered. We first consider the case of ties in preference lists. Nasre proved that the problem of counting the number of popular matching is #P-hard when there are ties. We give an...

We determine the computational power of preparing Projected Entangled Pair States (PEPS), as well as the complexity of classically simulating them, and generally the complexity of contracting tensor networks. While creating PEPS allows to solve PP problems, the latter two tasks are both proven to be #P-complete. We further show how PEPS can be used to approximate ground states of gapped Hamilto...

Let p be a prime. Given a polynomial in Fpm [x] of degree d over the finite field Fpm , one can view it as a map from Fpm to Fpm , and examine the image of this map, also known as the value set. In this paper, we present the first non-trivial algorithm and the first complexity result on explicitly computing the cardinality of this value set. We show an elementary connection between this cardina...

Graph has become a widely used structure to model data. Unfortunately, data are inherently with uncertainty because of the occurrence of noise and incompleteness in data collection. This is why uncertain graphs catch much attention of researchers. However, the uncertain graph models in existing works assume all edges in a graph are independent of each other, which dose not really make sense in ...

The study of infection processes is an important field of science both from the theoretical and the practical point of view, and has many applications. In this paper we focus on the popular Independent Cascade model and its generalization. Unfortunately the exact computation of infection probabilities is a #P-complete problem [8], so one cannot expect fast exact algorithms. We propose several m...

The HIGH DEGREE SUBGRAPH problem is to find a subgraph H of a graph G such that the minimum degree of H is as large as possible. This problem is known to be P-hard so that parallel approximation algorithms are very important for it. Our first goal is to determine how effectively the approximation algorithm based on a well-known extremal graph result parallelizes. In particular, we show that two...

The problem of devising an algorithm for counting the number of perfect matchings in bipartite graphs has a long history. Apparently the first algorithm (which works only in planar graphs) was presented in 1961 [8]. Then Valiant in 1979 showed that the problem is #P-complete, meaning that no polynomial-time algorithm exists for the problem, unless P = NP [11]. After that, people focused on deve...

Abstract Central exclusive diffractive production (CEDP) of proton–anti-proton pairs is calculated in the Regge-eikonal approach taking into account continuum and possible $$f_0(2100)$$ f 0 ( 2100 ) </mml:mat...

To find the most influential nodes for viral marketing, several models have been proposed to describe the influence propagation process. Among them, the Independent Cascade (IC) Model is most widelystudied. However, under IC model, computing influence spread (i.e., the expected number of nodes that will be influenced) for each given seed set has been proved to be #P-hard. To that end, in this p...