Antoine Bossard

The Set-to-Set Disjoint-Path Problem in Perfect Hierarchical Hypercubes

The perfect hierarchical hypercube (HHC) interconnection network has been introduced in the literature recently. An HHC can connect many nodes while retaining a low degree and a small diameter. It is thus a suitable topology for interconnection networks of massively parallel systems. We describe in this paper an algorithm solving the set-to-set disjoint-path routing problem in perfect HHCs. In an HHC2m+m, given two sets of m+1 nodes S and D, the proposed algorithm can find m+1 node-disjoint paths between the nodes of S and the nodes of D of lengths at most (m+1) (2m + m + 4) + 3 in O(m2 22m) time complexity.

Node-to-Set Disjoint-Path Routing in Hierarchical Cubic Networks

Hypercubes are a simple topology frequently used as interconnection network of parallel systems. However, hypercubes connecting a significant number of nodes also have an impractically high number of edges. To address this issue, Ghose and Desai introduced a new topology, hierarchical cubic networks, containing almost half many edges than a hypercube of the same size. In this paper, we describe a node-to-set disjoint-path routing algorithm in a hierarchical cubic network HCN(n) finding node-disjoint paths between one source node and k (k≤n+1) destination nodes in O(knlog k) time complexity. Generated paths have lengths of at most 3n+k+3.

Node-to-Set Disjoint-path Routing in Metacube

The metacube interconnection network introduced a few years ago has some very interesting properties: it has a short diameter similar to the hypercube, and its degree is much lower than that of a hypercube of the same size. In this paper, we describe an efficient algorithm for finding disjoint paths between one source node and at most m+k target nodes in a metacube MC(k, m) excluding MC(*,1), MC(2,2), MC(3,2) and MC(3,3). We show that we can find m+k disjoint paths between the source node and the m+k targets of length at most metacube diameter plus (k+4) with time complexity of order of metacube degree times its diameter.

Supporting reconstruction of the blood vessel network using graph theory: An abstraction method

The blood vessel network (BVN) has a complex structure. As this structure is unique for each individual, it is not possible to establish a general model for the BVN. However, many medical applications do rely on this structure. For example, a drug delivery system would be greatly improved if it could control the drug flow towards destination. To address this BVN structure issue, several reconstruction methods have been introduced. In this paper, we describe an abstraction method supporting BVN reconstruction by using graph theory. Starting from an original BVN reconstruction, we define the so-called induced graph of that reconstruction, allowing for an efficient analysis. By applying this method, we were able to improve an original BVN reconstruction of a human kidney by pointing out probable errors inside that original reconstruction.

A New Node-to-Set Disjoint-Path Algorithm in Perfect Hierarchical Hypercubes

The perfect hierarchical hypercube (HHC) interconnection network, also known as the cube-connected cube, was introduced as a topology for large parallel computers. One of its interesting properties is that it can connect many nodes while retaining a small diameter and a low degree. The first node-to-set disjoint-path routing algorithm in perfect HHCs was previously introduced by Bossard et al. [(2011) Node-to-Set Disjoint-Path Routing in Perfect Hierarchical Hypercubes. Proc. 11th Int. Conf. Computational Science, Tsukuba, Japan, June 1–3. Elsevier, Amsterdam]. In this paper, we propose a novel solution to the node-to-set disjoint-path routing problem in HHC. Inside a (2m + m)-dimensional HHC, we shall describe an algorithm that can find disjoint paths between a source node and at most m + 1 destination nodes of maximum length O(2m), significantly shorter than the maximum path length O(m2m) of Bossard et al. [(2011) Node-to-Set Disjoint-Path Routing in Perfect Hierarchical Hypercubes. Proc. 11th Int. Conf. Computational Science, Tsukuba, Singapore, June 1–3. Elsevier, Amsterdam].

The decycling problem in hierarchical cubic networks

Hierarchical cubic networks (HCN) have been introduced as interconnection networks for massively parallel systems. This topology is based on hypercubes, and thus benefits from their desirable properties such as a small diameter. However, an HCN supersedes a hypercube in many ways: for instance, the number of links per node in an HCN is significantly lower than that of a hypercube of the same size, while their diameters remain similar. In this paper we address the decycling problem in an HCN. It consists in finding a node set of minimum size such that excluding these nodes from the network ensures an acyclic (cycle-free) network. This is a critical problem with many applications, and notably in parallel computing as it allows for the prevention of resource allocation issues such as deadlocks, livelocks and starvations. We propose an efficient algorithm generating in an

k-pairwise disjoint paths routing in perfect hierarchical hypercubes

n

Node-to-set disjoint paths routing in a metacube

n-dimensional HCN a decycling set of at most