Nils Schweer

No-break dynamic defragmentation of reconfigurable devices

We propose a new method for defragmenting the module layout of a reconfigurable device, enabled by a novel approach for dealing with communication needs between relocated modules and with inhomogeneities found in commonly used FPGAs. Our method is based on dynamic relocation of module positions during runtime, with only very little reconfiguration overhead; the objective is to maximize the length of contiguous free space that is available for new modules. We describe a number of algorithmic aspects of good defragmentation, and present an optimization method based on tabu search. Experimental results indicate that we can improve the quality of module layout by roughly 50% over static layout. Among other benefits, this improvement avoids unnecessary rejection of modules.

Integer point sets minimizing average pairwise L1 distance: What is the optimal shape of a town?

An n-town, n@?N, is a group of n buildings, each occupying a distinct position on a 2-dimensional integer grid. If we measure the distance between two buildings along the axis-parallel street grid, then an n-town has optimal shape if the sum of all pairwise Manhattan distances is minimized. This problem has been studied for cities, i.e., the limiting case of very large n. For cities, it is known that the optimal shape can be described by a differential equation, for which no closed-form solution is known. We show that optimal n-towns can be computed in O(n^7^.^5) time. This is also practically useful, as it allows us to compute optimal solutions up to n=80.

Dynamic Defragmentation of Reconfigurable Devices

We propose a new method for defragmenting the module layout of a reconfigurable device, enabled by a novel approach for dealing with communication needs between relocated modules and with inhomogeneities found in commonly used FPGAs. Our method is based on dynamic relocation of module positions during runtime, with only very little reconfiguration overhead; the objective is to maximize the length of contiguous free space that is available for new modules. We describe a number of algorithmic aspects of good defragmentation, and present an optimization method based on tabu search. Experimental results indicate that we can improve the quality of module layout by roughly 50% over the static layout. Among other benefits, this improvement avoids unnecessary rejections of modules.

Online Square Packing

We analyze the problem of packing squares in an online fashion: Given a semi-infinite strip of width 1 and an unknown sequence of squares of side length in [0,1] that arrive from above, one at a time. The objective is to pack these items as they arrive, minimizing the resulting height. Just like in the classical game of Tetris, each square must be moved along a collision-free path to its final destination. In addition, we account for gravity in both motion and position. We apply a geometric analysis to establish a competitive factor of 3.5 for the bottom-left heuristic and present a

ReCoNodes—Optimization Methods for Module Scheduling and Placement on Reconfigurable Hardware Devices

\frac{34}{13} \approx 2.6154

Virtual area management: Multitasking on dynamically partially reconfigurable devices

-competitive algorithm.

A Competitive Strategy for Distance-Aware Online Shape Allocation

Placement and scheduling are recognized as the most important problems when exploiting the benefit of partially reconfigurable devices such as FPGAs. For example, dynamically loading and unloading modules onto an FPGA causes fragmentation, and—in turn—may decrease performance. To counteract this effect, we use methods from algorithmics and mathematical optimization to increase the performance and present algorithms for placing, scheduling, and defragmenting modules on FPGAs. Taking communication between modules into account, we further present strategies to minimize communication overhead. Finally, we consider scheduling module requests with time-varying resource demands.

Maintaining arrays of contiguous objects

Every year the computing resources available on dynamically partially reconfigurable devices increase enormously. In the near future, we expect many applications to run on a single reconfigurable device. In this paper, we present a concept for multitasking on dynamically partially reconfigurable systems called virtual area management. We explain its advantages, show its challenges, and discuss possible solutions. Furthermore, we investigate one problem in more detail: Packing modules with time-varying resource requests. This problem from the reconfigurable computing field results in a completely new optimization problem not tackled before. ILP-based and heuristic approaches are compared in an experimental study and the drawbacks and benefits discussed.

Online Square Packing with Gravity

We consider the following online allocation problem: Given a unit square S, and a sequence of numbers n i ∈ {0,1} with \(\sum_{j=0}^i n_j\leq 1\); at each step i, select a region C i of previously unassigned area n i in S. The objective is to make these regions compact in a distance-aware sense: minimize the maximum (normalized) average Manhattan distance between points from the same set C i . Related location problems have received a considerable amount of attention; in particular, the problem of determining the “optimal shape of a city”, i.e., allocating a single n i has been studied, both in a continuous and a discrete setting. We present an online strategy, based on an analysis of space-filling curves; for continuous shapes, we prove a factor of 1.8092, and 1.7848 for discrete point sets.