We implement two recently published quantum amplitude estimation algorithms on the IBM quantum device to analyze and discuss advantages of each of these algorithms from the perspective of its performance on a quantum ...
详细信息
Regularized optimal mass transport (rOMT) problem adds a diffusion term to the continuity equation in the original dynamic formulation of the optimal mass transport (OMT) problem proposed by Benamou and Brenier. We sh...
详细信息
Shape grammars have become established as a method of generating designs (images), especially in architecture, engineering and product design. Most shape grammar systems generate images in a way that is not always reg...
详细信息
Edge connectivity of a graph is one of the most fundamental graph-theoretic concepts. The celebrated tree packing theorem of Tutte and Nash-Williams from 1961 states that every k-edge connected graph G contains a coll...
详细信息
Edge connectivity of a graph is one of the most fundamental graph-theoretic concepts. The celebrated tree packing theorem of Tutte and Nash-Williams from 1961 states that every k-edge connected graph G contains a collection T of bk/2c edge-disjoint spanning trees, that we refer to as a tree packing;the diameter of the tree packing T is the largest diameter of any tree in T . A desirable property of a tree packing, that is both sufficient and necessary for leveraging the high connectivity of a graph in distributed communication networks, is that its diameter is low. Yet, despite extensive research in this area, it is still unclear how to compute a tree packing, whose diameter is sublinear in |V (G)|, in a low-diameter graph G, or alternatively how to show that such a packing does not exist. In this paper, we provide first non-trivial upper and lower bounds on the diameter of tree packing. We start by showing that, for every k-edge connected n-vertex graph G of diameter D, there is a tree packing T containing Ω(k) trees, of diameter O((101k log n)D), with edge-congestion at most 2. Karger’s edge sampling technique demonstrates that, if G is a k-edge connected graph, and G[p] is a subgraph of G obtained by sampling each edge of G independently with probability p = Θ(log n/k), then with high probability G[p] is connected. We extend this result to show that the diameter of G[p] is bounded by O(kD(D+1)/2) with high probability. This immediately implies that for every k-edge connected n-vertex graph G of diameter D, there is a tree packing T containing Ω(k/ log n) edge-disjoint trees of diameter at most O(kD(D+1)/2) each. We complement the above two results by showing that they are nearly tight: namely, that there is a k-edge connected graph of diameter 2D, such that any packing of k/α trees with edge-congestion η contains at least one tree of diameter Ω ((k/(2αηD))D), for any k, α and η. Lastly, we show that if, for every pair u, v of vertices in a given graph G, there is
We correct the expression for the worst-case error derived in [Kuo, Wasilkowski, Woźniakowski, Construct. Approx. 30 (2009), 475–493] and explain that the main theorem of the paper holds with enlarged constants.
We correct the expression for the worst-case error derived in [Kuo, Wasilkowski, Woźniakowski, Construct. Approx. 30 (2009), 475–493] and explain that the main theorem of the paper holds with enlarged constants.
Combinatorial vector fields on simplicial complexes introduced by Robin Forman constitute a combinatorial analogue of classical flows. They have found numerous and varied applications in recent years. Yet, their forma...
详细信息
Infinite Gray code has been introduced by Tsuiki [Ts02] as a redundancy-free representation of the reals. In applications the signed digit representation is mostly used which has maximal redundancy. Tsuiki presented a...
详细信息
This paper describes a hierarchical multi-scale scheme that aims to efficiently predict the mechanical behavior of graphene-based polymer nanocomposites with continuum models using data from detailed atomistic molecul...
详细信息
暂无评论