Although distributed computing over a network of computers has become a reality, its success mainly depends on the performance of the underlying network. In this paper, we consider the problem of designing a local area network with specified cost and performance constraints. The cost and performance of a local area network (LAN) are directly related to its topology. Using the a priori knowledge of the approximate number of users of the network and the kind of communication traffic that must be supported, the designer can optimize the design of the of a LAN for superior performance. Design decisions include the number of LAN segments, number of bridges, assignment of users to segments, and the method to interconnect the segments through bridges. In case of ATM networks, the decisions are regarding the number of ATM switches, the assignment of hosts to switches, and the way to connect switches through cross-connects. While assigning too many users to the same segment may cause large delays due to the sharing of network bandwidth, splitting the LAN into too many segments will increase the cost of the LAN. We report a greedy heuristic algorithm for Local Area Network Design. We propose an interesting method to construct good initial solutions to the topology design problem using a heuristic method which is based on the three-opt technique for solving the travelling salesperson problem. Our experimental results indicate that the heuristic algorithm finds good solutions.Unlike a multiprocessor, a distributed computing environment grows or shrinks dynamically. The number of users may grow way beyond the number for which the network was originally designed, resulting in a performance * Dilip and Anubhav were M.Tech students of Computer Technology in the Department of Electrical Engineering when this work was carried out. An equipment grant from Sun Microsystems is gratefully acknowledged.degradation. In such a situation, a complete redegin of the network may not be feasible without incurring a prolonged disruption in service and a significant rewiring cost. What is desirable is an incremental redesign, which preserves most features of the existing network and requires as little rewiring as possible. We consider the problem of network redesign as an optimisation problem and present heuristic algorithms for the problem. The algorithm works in four phases which correspond to four network redesign options that are progressively more expensive. Thus, while the first phase tries to achieve better network performance by user reassignment, the fourth phase calls for creation of an additional LAN segment using an additional bridge. Our heuristic algorithm is greedy in that it chooses a more expensive redesign technique only when the more economical ones fail to provide the desired performance. We present experimental results of an implementation of our redesign heuristic.

An NP-complete coloring or homomorphism problem may become polynomial time solvable when restricted to graphs with degrees bounded by a small number, but remain NP-complete if the bound is higher. For instance, 3-colorability of graphs with degrees bounded by 3 can be decided by Brooks' theorem, while for graphs with degrees bounded by 4, the 3-colorability problem is NP-complete. We investigate an analogous phenomenon for digraphs, focusing on the three smallest digraphs H with NP-complete H-colorability problems. It turns out that in all three cases the H-coloring problem is polynomial time solvable for digraphs with degree bounds ∆ + ≤ 1, ∆ − ≤ 2 (or ∆ + ≤ 2, ∆ − ≤ 1). On the other hand with degree bounds ∆ + ≤ 2, ∆ − ≤ 2, all three problems are again NP-complete. A conjecture proposed for graphs H by Feder, Hell and Huang states that any variant of the H-coloring problem which is NP-complete without degree constraints is also NP-complete with degree constraints, provided the degree bounds are high enough. Our study is the first confirmation that the conjecture may also apply to digraphs.

Oracle Database In-Memory (DBIM) accelerates analytic workload performance by orders of magnitude through an inmemory columnar format utilizing techniques such as SIMD vector processing, in-memory storage indexes, and optimized predicate evaluation and aggregation. With Oracle Database 12.2, Database In-Memory is further enhanced to accelerate analytic processing through a novel lightweight mechanism known as Dynamic In-Memory Expressions (DIMEs). The DIME mechanism automatically detects frequently occurring expressions in a query workload, and then creates highly optimized, transactionally consistent, in-memory columnar representations of these expression results. At runtime, queries can directly access these DIMEs, thus avoiding costly expression evaluations. Furthermore, all the optimizations introduced in DBIM can apply directly to DIMEs. Since DIMEs are purely in-memory structures, no changes are required to the underlying tables. We show that DIMEs can reduce query elapsed times by several orders of magnitude without the need for costly pre-computed structures such as computed columns or materialized views or cubes.

An NP-complete coloring or homomorphism problem may become polynomial time solvable when restricted to graphs with degrees bounded by a small number, but remain NP-complete if the bound is higher. We investigate an analogous phenomenon for digraphs, focusing on the three smallest digraphs H with NP-complete H-colorability problems. It turns out that in all three cases the H-coloring problem is polynomial time solvable for digraphs with in-degrees at most 1, regardless of the out-degree bound (respectively with out-degrees at most 1, regardless of the in-degree bound). On the other hand, as soon as both in-and out-degrees are bounded by constants greater than or equal to 2, all three problems are again NP-complete. Interestingly, the situation changes when we further restrict the inputs to be acyclic digraphs. In two of the three cases the NP-complete problems remain NP-complete. In the third case, the H-coloring problem turns out to be polynomial time solvable for acyclic digraphs with in-degrees at most 2, regardless of the out-degree bound (respectively with out-degrees at most 2, regardless of the in-degree bound). We also show that in this case as soon as both in-and out-degrees are bounded by constants greater than or equal to 3, the H-coloring problem is once again NP-complete, even for acyclic digraphs. A conjecture proposed for graphs H by Feder, Hell and Huang states that any variant of the H-coloring problem which is NP-complete without degree constraints is also NP-complete with degree constraints, provided the degree bounds are high enough. It has been verified for H-coloring of digraphs, but the degree bounds are quite high, and are stated in terms of the sum of in-and out-degrees. Our results confirm the conjecture with the best possible bounds that are needed for NP-completeness; moreover, they underscore the fact that the bound must apply separately to both the indegrees and the out-degrees.

No abstract