Sreyash Kenkre

Circumference, chromatic number and online coloring

Erdős conjectured that if G is a triangle free graph of chromatic number at least k≥3, then it contains an odd cycle of length at least k2−o(1) [13,15]. Nothing better than a linear bound ([3], Problem 5.1.55 in [16]) was so far known. We make progress on this conjecture by showing that G contains an odd cycle of length at least Ω(k log logk). Erdős’ conjecture is known to hold for graphs with girth at least five. We show that if a graph with girth four is C5 free, then Erdős’ conjecture holds. When the number of vertices is not too large we can prove better bounds on χ. We also give bounds on the chromatic number of graphs with at most r cycles of length 1 mod k, or at most s cycles of length 2 mod k, or no cycles of length 3 mod k. Our techniques essentially consist of using a depth first search tree to decompose the graph into ordered paths, which are then fed to an online coloring algorithm. Using this technique we give simple proofs of some old results, and also obtain several other results. We also obtain a lower bound on the number of colors which an online coloring algorithm needs to use to color triangle free graphs.

Recourse aware resource allocation for contingency planning in distributed service delivery

Remote delivery of services using geographically distributed service delivery locations has emerged as a popular and viable business model. Examples of services delivered in this manner are software services, business process outsourcing services, customer support centers, etc. The very nature of services and the fragile nature of the business environments in some of the delivery locations accentuates the need for business continuity. A key aspect of enabling business continuity is, at the time of a disruptive event, ability to reroute the services delivered from affected locations to unaffected locations while meeting their resource requirements. Such rerouting is called recourse. We highlight the need for recourse aware resource allocation. We study this problem from a computational viewpoint, present a new recourse aware resource allocation heuristic, and experimentally compare this to traditional resource allocation methods.

Reusable Resource Scheduling via Colored Interval Covering

Motivated by scheduling scenarios in large shared computing systems, we study the problem of reusable resource scheduling. In this problem, there are many resources, each specified by a capacity, duration, per-use cost, and an availability window comprising of a release time and a deadline. A resources can be reused multiple times within its availability window with each use being limited by the duration associated with the resource and incurring cost equal to per-use cost. Different uses of a resource have to be non-overlapping. Given a demand profile, the goal is to cover it by scheduling the resources within their availability windows while minimizing their total cost. Reusable resource scheduling is a generalization of the well known interval covering problem. We present approximation algorithms and hardness results for the reusable resource scheduling problem. While the interval cover problem is NP-hard, it can be solved optimally for the special case where all the resources have unit capacities. In contrast, we show that the reusable resource scheduling is NP-hard and APX-hard, even for the case where the resources have unit capacities and unit costs. The approximation algorithms are derived by considering the notion of colored interval coloring, which could be of independent interest.

Platform-independent robust query processing

To address the classical selectivity estimation problem in databases, a radically different approach called PlanBouquet was recently proposed in [3], wherein the estimation process is completely abandoned and replaced with a calibrated discovery mechanism. The beneficial outcome of this new construction is that, for the first time, provable guarantees are obtained on worst-case performance, thereby facilitating robust query processing.

Resiliency Analytics Framework for Service Delivery Organizations

Resiliency is a key word for a broad range of service delivery organizations. It is defined as the ability of an organization to rapidly adapt and effectively respond to the disruptions in its operations. A service delivery organization delivers a set of services which are essentially specified by their required set of resources. The organization sets up an infrastructural network of resources required for the service delivery and assigns to each service, its required set of resources. It also keeps sufficient residual capacity of the resources for the purpose of contingency planning. At the time of a disruptive incident, it reallocates the resources to the affected services from its residual capacity to keep the service running while the effects of the disruptions are reversed. Such actions of reallocating the resources to deal with disruptions to the original allocation are called recourse actions. We develop a framework that enables a data and analytics driven approach to achieve efficient recourse actions based resiliency. Our framework is based on abstractions of three important aspects of a service delivery organization, namely, the infrastructural network of resources, the set of services in terms of their requirements of resources, and the set of disruptive scenarios that an organization has to contend with. Our model also captures the different dependencies that exist within the infrastructure network. For instance, if the power supply is affected, our model allows us to infer all the other infrastructure resources which get affected as a consequence of the lack of power supply. There are no benchmark datasets to test the quality of resiliency analytics because of two reasons: nascency of research in this area and the classified nature of the organizational data required for such analytics. So, we have developed a simulation engine aimed at mimicking real-life organizations. We demonstrate how our framework can be used to proactively identify critical scenarios that could have adverse impact on the service delivery of an organization. We then show how such a knowledge can be used to make intelligent allocation of resources to the services so as to enable efficient recourse actions. These two analyses highlight that our framework can essentially serve as a decision support system for resiliency.

A concave path to low-overhead robust query processing

To address the classical selectivity estimation problem in database systems, a radically different query processing technique called PlanBouquet was proposed in 2014. In this approach, the estimation process is completely abandoned and replaced with a calibrated selectivity discovery mechanism. The beneficial outcome is that provable guarantees are obtained on worst-case execution performance, thereby facilitating robust query processing. An improved version of PlanBouquet, called SpillBound (SB), which significantly accelerates the selectivity discovery process, and provides platform-independent performance guarantees, was presented two years ago. Notwithstanding its benefits, a limitation of SpillBound is that its guarantees are predicated on expending enormous preprocessing efforts during query compilation, making it suitable only for canned queries that are invoked repeatedly. In this paper, we address this limitation by leveraging the fact that plan cost functions typically exhibit concave down behavior with regard to predicate selectivities. Specifically, we design FrugalSpillBound, which provably achieves extremely attractive tradeoffs between the performance guarantees and the compilation overheads. For instance, relaxing the performance guarantee by a factor of two typically results in at least two orders of magnitude reduction in the overheads. Further, when empirically evaluated on benchmark OLAP queries, the decrease in overheads is even greater, often more than three orders of magnitude. Therefore, FrugalSpillBound substantively extends robust query processing towards supporting ad-hoc queries. PVLDB Reference Format: Srinivas Karthik, Jayant R. Haritsa, Sreyash Kenkre, and Vinayaka Pandit. A Concave Path to Low-overhead Robust Query Processing. PVLDB, 11 (13): 2183-2195, 2018. DOI: https://doi.org/10.14778/3275366.3275368

On the Approximability of Digraph Ordering

Given an n-vertex digraph D = (V, A) the Max-k-Ordering problem is to compute a labeling l: V → [k] maximizing the number of forward edges, i.e. edges (u,v) such that l(u) 0, Max-k-Ordering has an LP integrality gap of 2 − e for \(n^{\Omega\left(\left.1\middle/\log\log k\right.\right)}\) rounds of the Sherali-Adams hierarchy.

Budget utilization for improved business contingency planning in service delivery

Service delivery using geographically distributed delivery locations has emerged as a mature methodology of service delivery. The fragile nature of business environments at the delivery locations has resulted Business Continuity Planning methodology in becoming a key differentiator between service delivery organizations. Increasingly, these organizations are actively seeking to allocate funds for improving their BCP posture by procuring resources. However, the conventional techniques of cost benefit analysis while allocating budget for the procurement of resources do not take into account the special need of factoring for resumption plans while procurement of resources for BCP. In this paper we explore the issues faced in utilizing budgets for BCP, and suggest a broad methodology that may be used for optimal budget utilization.

Algorithmic aspects of planning under uncertainty for service delivery organizations

Remote delivery of services using geographically distributed service delivery locations has emerged as a popular and viable business model. Examples of services delivered in this manner are software services, business process outsourcing services, customer support centers, etc. The very nature of services and the fragile nature of the business environments in global delivery locations accentuates the role of uncertainty in planning for business continuity. We model the problem of critical service contingency planning based on recourse actions. We present an O(logn)-approximation algorithm, generalizations to other planning problems under uncertainty, and present preliminary empirical results.