Any graph $G$ with chromatic number $k$ can be obtained using a Hajós-type construction, i.e., by iteratively performing the Hajós merge and vertex identification operations on a sequence of graphs starting with $K_k$. Finding such constructions for a given graph or family of graphs is a challenging task. In this paper, we show that for a large class of Hajós merges and for any identification of a pair of vertices having distance at least five from each other, the resulting graph has an $S^1$-wedge summand in its neighborhood complex. Our results imply that for a bridgeless graph $G$ with a highly connected neighborhood complex, the final step in a Hajós construction must be a vertex identification with vertices at short distance from each other. We investigate this restriction in detail. We also introduce two graph construction algorithms using Hajós-type operations. We discuss the results of computational experiments in which we investigate the rank of the first homology group of the neighborhood complexes of graphs generated using these algorithms.

Multi-core programming remains a major software development and maintenance challenge because of data races, deadlock, non-deterministic failures and complex performance issues. In this paper, we describe EXCITE-VM, a system that provides snapshot isolation transactions on shared memory to facilitate programming and to improve the performance of parallel applications. With snapshots, an application thread is not exposed to the committed changes of other threads until it receives the updates by explicitly creating a new snapshot. Snapshot isolation enables low overhead lockless read operations and improves fault tolerance by isolating each thread from the transient, uncommitted writes of other threads. This paper describes how EXCITE-VM implements snapshot isolation transactions efficiently by manipulating virtual memory mappings and using a novel copy-on-read mechanism with a customized page cache. Compared to conventional software transactional memory systems, EXCITE-VM provides up to 2.2x performance improvement for the STAMP benchmark suite and up to 1000x speedup for a modified benchmark having long running read-only transactions. Furthermore, EXCITE-VM achieves a 2x performance improvement on a Memcached benchmark and the Yahoo Cloud Server Benchmarks. Finally, EXCITE-VM improves fault tolerance and offers features such as low-overhead concurrent audit and analysis.

We investigate the arithmetic-geometric structure of the lecture hall cone $L_n \ := \ \big\{\lambda\in \mathbb{R}^n: \, 0\leq \frac{\lambda_1}{1}\leq \frac{\lambda_2}{2}\leq \frac{\lambda_3}{3}\leq \cdots \leq \frac{\lambda_n}{n}\big\}$. We show that $L_n$ is isomorphic to the cone over the lattice pyramid of a reflexive simplex whose Ehrhart $h^*$-polynomial is given by the $(n-1)$st Eulerian polynomial and prove that lecture hall cones admit regular, flag, unimodular triangulations. After explicitly describing the Hilbert basis for $L_n$, we conclude with observations and a conjecture regarding the structure of unimodular triangulations of $L_n$, including connections between enumerative and algebraic properties of $L_n$ and cones over unit cubes.

The area of proof-based verified computation (outsourced computation built atop probabilistically checkable proofs and cryptographic machinery) has lately seen renewed interest. Although recent work has made great strides in reducing the overhead of naive applications of the theory, these schemes still cannot be considered practical. A core issue is that the work for the server is immense, in general; it is practical only for hand-compiled computations that can be expressed in special forms.

When a client outsources a job to a third party (e.g., the cloud), how can the client check the result, without re-executing the computation? Recent work in proof-based verifiable computation has made significant progress on this problem by incorporating deep results from complexity theory and cryptography into built systems. However, these systems work within a stateless model: they exclude computations that interact with RAM or a disk, or for which the client does not have the full input.