Related papers: The Complexity of Contracting Planar Tensor Networ…
We present improved distributed algorithms for triangle detection and its variants in the CONGEST model. We show that Triangle Detection, Counting, and Enumeration can be solved in $\tilde{O}(n^{1/2})$ rounds. In contrast, the previous…
We provide a simple new randomized contraction approach to the global minimum cut problem for simple undirected graphs. The contractions exploit 2-out edge sampling from each vertex rather than the standard uniform edge sampling. We…
Many combinatorial problems can be solved in time $O^*(c^{tw})$ on graphs of treewidth $tw$, for a problem-specific constant $c$. In several cases, matching upper and lower bounds on $c$ are known based on the Strong Exponential Time…
We present a conceptually clear and algorithmically useful framework for parameterizing the costs of tensor network contraction. Our framework is completely general, applying to tensor networks with arbitrary bond dimensions, open legs, and…
Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for…
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…
We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut…
Let $\Lambda(T)$ denote the set of leaves in a tree $T$. One natural problem is to look for a spanning tree $T$ of a given graph $G$ such that $\Lambda(T)$ is as large as possible. This problem is called maximum leaf number, and it is a…
The maximum/minimum bisection problems are, given an edge-weighted graph, to find a bipartition of the vertex set into two sets whose sizes differ by at most one, such that the total weight of edges between the two sets is…
This paper presents efficient distributed algorithms for a number of fundamental problems in the area of graph sparsification: We provide the first deterministic distributed algorithm that computes an ultra-sparse spanner in…
We study the problem of finding a maximum cardinality minimal separator of a graph. This problem is known to be NP-hard even for bipartite graphs. In this paper, we strengthen this hardness by showing that for planar bipartite graphs, the…
In the Directed Steiner Network problem, the input is a directed graph G, a subset T of k vertices of G called the terminals, and a demand graph D on T. The task is to find a subgraph H of G with the minimum number of edges such that for…
The tensor network variety is a variety of tensors associated to a graph and a set of positive integer weights on its edges, called bond dimensions. We determine an upper bound on the dimension of the tensor network variety. A refined upper…
We prove that a connected planar graph with $n$ vertices and $n+\mu$ edges has a vertex separator of size $O( \sqrt{\mu} + 1)$, and this separator can be computed in linear time.
We consider the problem of computing compact routing tables for a (weighted) planar graph $G:= (V, E,w)$ in the PRAM, CONGEST, and the novel HYBRID communication model. We present algorithms with polylogarithmic work and communication that…
In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost of…
We study Clustered Planarity with Linear Saturators, which is the problem of augmenting an $n$-vertex planar graph whose vertices are partitioned into independent sets (called clusters) with paths - one for each cluster - that connect all…
This paper accompanies with our recent work on quantum error correction (QEC) and entanglement spectrum (ES) in tensor networks (arXiv:1806.05007). We propose a general framework for planar tensor network state with tensor constraints as a…
While multilinear algebra appears natural for studying the multiway interactions modeled by hypergraphs, tensor methods for general hypergraphs have been stymied by theoretical and practical barriers. A recently proposed adjacency tensor is…