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- Tian-Yi Jiang, Ziv Scully, Yan X. Zhang
- SIAM J. Discrete Math.
- 2015

The parallel chip-firing game is an automaton on graphs in which vertices “fire” chips to their neighbors. This simple model contains much emergent complexity and has many connections to different areas of mathematics. In this work, we study firing sequences, which describe each vertex’s interaction with its neighbors in this game. First, we introduce the… (More)

The parallel chip-firing game is an automaton on graphs in which vertices “fire” chips to their neighbors. This simple model, analogous to sandpiles forming and collapsing, contains much emergent complexity and has connections to different areas of mathematics including self-organized criticality and the study of the sandpile group. In this work, we study… (More)

- Ziv Scully, Guy E. Blelloch, Mor Harchol-Balter, Alan Scheller-Wolf
- SIGMETRICS Performance Evaluation Review
- 2017

We consider optimal job scheduling where each job consists of multiple tasks, each of unknown duration, with precedence constraints between tasks. A job is not considered complete until all of its tasks are complete. Traditional heuristics, such as favoring the job of shortest expected remaining processing time, are suboptimal in this setting. Furthermore,… (More)

The parallel chip-firing game is an automaton on graphs in which vertices “fire” chips to their neighbors when they have enough chips to do so. In this work we first characterize positions that repeat every 2 turns. Using this we determine the eventual periods of games on trees given only the total number of chips. We introduce the concepts of motorized… (More)

- Ziv Scully, Adam Chlipala
- POPL
- 2017

Most popular Web applications rely on persistent databases based on languages like SQL for declarative specification of data models and the operations that read and modify them. As applications scale up in user base, they often face challenges responding quickly enough to the high volume of requests. A common aid is caching of database results in the… (More)

- Tanya Khovanova, Ziv Scully
- ArXiv
- 2012

Efficient matrix determinant calculations have been studied since the 19th century. Computers expand the range of determinants that are practically calculable to include matrices with symbolic entries. However, the fastest determinant algorithms for numerical matrices are often not the fastest for symbolic matrices with many variables. We compare the… (More)

- Sheela Devadas, Masahiro Namiki, +13 authors Damien Jiang
- 2011

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