Dichotomy for tree-structured trigraph list homomorphism problems

Trigraph list homomorphism problems (also known as list matrix partition problems) have generated recent interest, partly because there are concrete problems that are not known to be polynomial time solvable or NP-complete. Thus while digraph list homomorphism problems enjoy dichotomy (each problem is NP-complete or polynomial time solvable), such dichotomy is not necessarily expected for trigraph list homomorphism problems. However, in this paper, we identify a large class of trigraphs for which list homomorphism problems do exhibit a dichotomy. They consist of trigraphs with a tree-like structure, and, in particular, include all trigraphs whose underlying graphs are trees. In fact, we show that for these tree-like trigraphs, the trigraph list homomorphism problem is polynomially equivalent to a related digraph list homomorphism problem. We also describe a few examples illustrating that our conditions defining tree-like trigraphs are not unnatural, as relaxing them may lead to harder problems

A Memory Contention Responsive Hash Join Algorithm Design and Implementation on Apache AsterixDB

Efficient data management is crucial in complex computer systems, and Database Management Systems (DBMS) are indispensable for handling and processing large datasets. In DBMSs that concurrently execute multiple queries, adapting to varying workloads is desirable. Yet, predicting the fluctuating quantity and size of queries in such environments proves challenging. Over-allocating resources to a single query can impede the execution of future queries while under-allocating resources to a query expecting increased workload can lead to significant processing delays. Moreover, join operations place substantial demands on memory. This resource’s availability fluctuates as queries enter and exit the DBMS. The development of join operators capable of dynamically adapting to memory fluctuations is a complex undertaking, with few recent authors proposing memory-adaptive algorithms. This scarcity of proposals suggests the inherent difficulty in designing, implementing, and analyzing such algorithms. This thesis proposes a new memory adaptive Hash-Based join algorithm extended from designs presented by prior authors. This algorithm is implemented and experimented with in a real DBMS environment to evaluate its memory fluctuation responsiveness. A mathematical model for the increase in I/O caused by it is proposed and compared with actual results. The impacts of memory variation and frequence of memory updates reveal the importance of this thesis for further development of memory adaptive algorithms