In this paper, we look at the complexity of designing algorithms without any bank conflicts in the shared memory of Graphical Processing Units (GPUs). Given input of size $n$, $w$ processors and $w$ memory banks, we study three fundamental problems: sorting, permuting and $w$-way partitioning (defined as sorting an input containing exactly $n\/w$ copies of every integer in $[w]$). We solve sorting in optimal $O(frac{n}{w} log n)$ time. When $n ge w^2$, we solve the partitioning problem optimally in $O(n\/w)$ time. We also present a general solution for the partitioning problem which takes $O(frac{n}{w} log^3_{n\/w} w)$ time. Finally, we solve the permutation problem using a randomized algorithm in $O(frac{n}{w} logloglog_{n\/w} n)$ time. Our results show evidence that when working with banked memory architectures, there is a separation between these problems and the permutation and partitioning problems are not as easy as simple parallel scanning.<\/p>\n","protected":false},"excerpt":{"rendered":"
In this paper, we look at the complexity of designing algorithms without any bank conflicts in the shared memory of Graphical Processing Units (GPUs). Given input of size $n$, $w$ processors and $w$ memory banks, we study three fundamental problems: sorting, permuting and $w$-way partitioning (defined as sorting an input containing exactly $n\/w$ copies of […]<\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[36,11,3],"tags":[1787,1782,67,9],"class_list":["post-14241","post","type-post","status-publish","format-standard","hentry","category-algorithms","category-computer-science","category-paper","tag-algorithms","tag-computer-science","tag-performance","tag-sorting"],"views":2043,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/14241","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=14241"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/14241\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14241"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14241"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14241"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}