Brian Tagiku

Minimizing Average Shortest Path Distances via Shortcut Edge Addition

We consider adding k shortcut edges (i.e. edges of small fixed length *** *** 0) to a graph so as to minimize the weighted average shortest path distance over all pairs of vertices. We explore several variations of the problem and give O (1)-approximations for each. We also improve the best known approximation ratio for metric k -median with penalties, as many of our approximations depend upon this bound. We give a

Online Multidimensional Load Balancing

(1+2\frac{(p+1)}{\beta(p+1)-1},\beta)

Fault tolerant placement and defect reconfiguration for nano-FPGAs

-approximation with runtime exponential in p . If we set β = 1 (to be exact on the number of medians), this matches the best current k -median (without penalties) result.

The survivability of design-specific spare placement in FPGA architectures with high defect rates

Energy efficient algorithms are becoming critically important, as huge data centers and server farms have increasing impact on monetary and environmental costs. Motivated by such issues, we study online load balancing from an energy perspective. Our framework extends recent work by Khuller, Li, and Saha (SODA 2010) to the online model. We are given m machines, each with some energy activation cost c i and d dimensions (i.e., components). There are n jobs which arrive online and must be assigned to machines. Each job induces a load on its assigned machine along each dimension. We must select machines to activate so that the total activation cost of the machines falls within a budget B and the largest load over all machines and dimensions (i.e., the makespan) by assigning jobs to active machines is at most Λ.

Coupled and k-Sided Placements: Generalizing Generalized Assignment

When manufacturing nano-devices, defects are a certainty and reliability becomes a critical issue. Until now, the most pervasive methods used to address reliability, involve injecting spare resources. However, these methods use predetermined spare placement that is not optimized for each netlist. This is the first work (to the best of our knowledge) that addresses the problem of fault tolerance for nano-FPGAs at the placement stage; fault tolerant placements are generated that are amenable to fast defect reconfiguration through replacement of defective logic elements with spares. We propose a simulated-annealing based placement algorithm that produces placements with the objective of maximizing the chances of successful recovery from faults in logic elements within the circuitpsilas timing constraints. In addition, our study of the fault reconfiguration problem shows it is NP-Complete, and we propose a fast scheme for achieving a good reconfiguration solution for a random or clustered fault map. Experimental results show that these techniques can increase the probability of successful fault reconfiguration by 55% (compared to a uniform spare distribution scheme), without significantly degrading the circuit performance.

Approximations for Aligned Coloring and Spillage Minimization in Interval and Chordal Graphs

We address the problem of optimizing fault tolerance in FPGA architectures with high defect rates (such as nano-FPGAs) without significantly degrading performance. Our methods address fault tolerance during the placement and reconfiguration stages of FPGA programming. First, we provide several complexity results for both the fault reconfiguration and fault-tolerance placement problems. Then, we propose a placement algorithm which, in the presence of randomly generated faults, optimizes spare placement to maximize the probability that the FPGA can be reconfigured to meet a specified timing constraint. We also give heuristics for reconfiguration after faults have been detected. Despite the hardness results for both the placement and reconfiguration problems, we show our heuristics perform well in simulation (in one scenario, increasing the probability of successful reconfiguration by as much as 55% compared to a uniform spare placement).

Streaming k -means on well-clusterable data

In modern data centers and cloud computing systems, jobs often require resources distributed across nodes providing a wide variety of services. Motivated by this, we study the Coupled Placement problem, in which we place jobs into computation and storage nodes with capacity constraints, so as to optimize some costs or profits associated with the placement. The coupled placement problem is a natural generalization of the widely-studied generalized assignment problem (GAP), which concerns the placement of jobs into single nodes providing one kind of service. We also study a further generalization, the k-Sided Placement problem, in which we place jobs into k-tuples of nodes, each node in a tuple offering one of k services.

Coupled and k-sided placements: generalizing generalized assignment

We consider the problem of aligned coloring of interval and chordal graphs. These problems have substantial applications to register allocation in compilers and have recently been proven NP-Hard. We provide the first constant approximations: a

Energy-efficient mobile data transport via online multi-network packet scheduling

\frac{4}{3}

The approximability of resource allocation problems in computer system design

-approximation for interval graphs and a