Graph pebbling is a network optimization model for transporting discrete resources that are consumed in transit: the movement of 2 pebbles across an edge consumes one of the pebbles. The pebbling number of a graph is the fewest number of pebbles t so that, from any initial configuration of t pebbles on its vertices, one can place a pebble on any given target vertex via such pebbling steps. It is known that deciding whether a given configuration on a particular graph can reach a specified target is NP-complete, even for diameter 2 graphs, and that deciding whether the pebbling number has a prescribed upper bound is Π[P over 2]-complete. On the other hand, for many families of graphs there are formulas or polynomial algorithms for computing pebbling numbers; for example, complete graphs, products of paths (including cubes), trees, cycles, diameter 2 graphs, and more. Moreover, graphs having minimum pebbling number are called Class 0, and many authors have studied which graphs are Class 0 and what graph properties guarantee it, with no characterization in sight. In this paper we investigate an important family of diameter 3 chordal graphs called split graphs; graphs whose vertex set can be partitioned into a clique and an independent set. We provide a formula for the pebbling number of a split graph, along with an algorithm for calculating it that runs in O(n[superscript β]) time, where β = 2ω/(ω + 1) [= over ∼] 1.41 and ω [= over ∼] 2.376 is the exponent of matrix multiplication. Furthermore we determine that all split graphs with minimum degree at least 3 are Class 0.

A two-part presentation from the ASU Library and Knowledge Enterprise Research Data Management Office. Presented at the 2023 Rocky Mountain Advanced Computing Consortium (RMACC).

Session 1: Data management planning is an integral step in the research data life cycle. Large amounts of data and lengthy code accompanying supercomputing runs are no exception. Planning before analysis will benefit research and the researcher by providing a clear strategy for collecting, storing, analyzing, and sharing the data at the end of the research cycle. Supercomputing can require significant storage beyond scratch space, but researchers typically need to be informed of what tools are appropriate and available. Framed within the planning phase of the life cycle, this presentation presents ASU’s Storage Selector as a quick and easy tool to find the most appropriate storage resources provided by the university to help researchers choose a proper storage and management solution for their research data at the right time in their project. We will also explore the DMP Tool, developed by the California Digital Library, which provides a resource-rich platform for writing data management plans, including institutional-specific guidance, feedback request, and public plans that can be used as guides.

Session 2: This presentation overviews the ongoing working relationship between the ASU Library Open Science and Scholarly Communication division, Research Data Management Office, and Research Computing. We will explore these teams’ interdisciplinary relationships and interdependence as the institution increasingly supports open science practices and initiatives. We will include case studies regarding the decision-making process, data-sharing decisions, and opportunities and challenges when transferring research data from a high-performance computing environment to the ASU Research Data Repository. Finally, we will share lessons learned as we intentionally shepherd research data from active project management and storage to final publication and preservation.