{"id":29685,"date":"1999-03-02T16:54:21","date_gmt":"1999-03-02T16:54:21","guid":{"rendered":"https:\/\/silvaco.com\/uncategorized\/advanced-pairwise-merging-algorithm-for-vlsi-floorplanning\/"},"modified":"2026-10-15T14:41:54","modified_gmt":"2026-10-15T21:41:54","slug":"advanced-pairwise-merging-algorithm-for-vlsi-floorplanning","status":"publish","type":"post","link":"https:\/\/silvaco.com\/ja\/simulation-standard\/advanced-pairwise-merging-algorithm-for-vlsi-floorplanning\/","title":{"rendered":"Advanced Pairwise Merging Algorithm for VLSI Floorplanning"},"content":{"rendered":"

Advanced Pairwise Merging Algorithm for VLSI Floorplanning<\/h1>\n

Introduction<\/p>\n

This paper concerns the problem of determining optimal placement of rectangular blocks within a rectangular area known as the packing or cutting-stock problem. This problem arises at then floorplanning stage of VLSI design.<\/p>\n

Assume that one is given n different types of rectangular blocks\u00a0R0,\u00a0R1,\u00a0… Rn ? 1,<\/b>\u00a0where\u00a0Ri\u00a0<\/b>is rectangle\u00a0hi\u00a0x wi<\/b>. The goal is to find non-overlapping placement of the blocks within rectangular area\u00a0A<\/b>\u00a0so that uncovered part of the area is as small as possible. The rectangle\u00a0A<\/b>\u00a0is referred to as\u00a0target area.<\/i>\u00a0Without loss of generality one can assume that a block of any type\u00a0Ri\u00a0<\/b>can fit in the target area. This problem is referred to as\u00a0packing problem.<\/i>\u00a0The problem is also known as\u00a0cutting stock<\/i>\u00a0problem. (It can be easily reformulated as problem of cutting rectangular sheet of material into rectangular pieces. We will use this name to refer to the problem as well.)<\/p>\n

\"\"<\/p>\n

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This paper concerns the problem of determining optimal placement of rectangular blocks within a rectangular area known as the packing or cutting-stock problem. This problem arises at then floorplanning stage of VLSI design.<\/p>\n","protected":false},"author":12,"featured_media":22100,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[7570],"tags":[],"class_list":["post-29685","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-simulation-standard","entry","has-media"],"yoast_head":"\nAdvanced Pairwise Merging Algorithm for VLSI Floorplanning - Silvaco<\/title>\n<meta name=\"description\" content=\"This paper concerns the problem of determining optimal placement of rectangular blocks within a rectangular area known as the packing or cutting-stock problem. 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This problem arises at then floorplanning stage of VLSI design.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/silvaco.com\/ja\/simulation-standard\/advanced-pairwise-merging-algorithm-for-vlsi-floorplanning\/\" \/>\n<meta property=\"og:site_name\" content=\"Silvaco\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/SilvacoSoftware\/\" \/>\n<meta property=\"article:published_time\" content=\"1999-03-02T16:54:21+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-10-15T21:41:54+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/silvaco.com\/wp-content\/uploads\/simulationstandard\/simstd_mar_1999_a2.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1280\" \/>\n\t<meta property=\"og:image:height\" content=\"1669\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Casey Molver\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@SilvacoSoftware\" \/>\n<meta name=\"twitter:site\" content=\"@SilvacoSoftware\" \/>\n<meta name=\"twitter:label1\" content=\"\u57f7\u7b46\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"Casey Molver\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u63a8\u5b9a\u8aad\u307f\u53d6\u308a\u6642\u9593\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/advanced-pairwise-merging-algorithm-for-vlsi-floorplanning\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/advanced-pairwise-merging-algorithm-for-vlsi-floorplanning\\\/\"},\"author\":{\"name\":\"Casey Molver\",\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/#\\\/schema\\\/person\\\/2763eb741ca5ac04477fdff50ed84c80\"},\"headline\":\"Advanced Pairwise Merging Algorithm for VLSI Floorplanning\",\"datePublished\":\"1999-03-02T16:54:21+00:00\",\"dateModified\":\"2026-10-15T21:41:54+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/advanced-pairwise-merging-algorithm-for-vlsi-floorplanning\\\/\"},\"wordCount\":172,\"image\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/advanced-pairwise-merging-algorithm-for-vlsi-floorplanning\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/silvaco.com\\\/wp-content\\\/uploads\\\/simulationstandard\\\/simstd_mar_1999_a2.jpg\",\"articleSection\":[\"Simulation Standard\"],\"inLanguage\":\"ja\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/advanced-pairwise-merging-algorithm-for-vlsi-floorplanning\\\/\",\"url\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/advanced-pairwise-merging-algorithm-for-vlsi-floorplanning\\\/\",\"name\":\"Advanced Pairwise Merging Algorithm for VLSI Floorplanning - Silvaco\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/advanced-pairwise-merging-algorithm-for-vlsi-floorplanning\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/simulation-standard\\\/advanced-pairwise-merging-algorithm-for-vlsi-floorplanning\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/silvaco.com\\\/wp-content\\\/uploads\\\/simulationstandard\\\/simstd_mar_1999_a2.jpg\",\"datePublished\":\"1999-03-02T16:54:21+00:00\",\"dateModified\":\"2026-10-15T21:41:54+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/silvaco.com\\\/ja\\\/#\\\/schema\\\/person\\\/2763eb741ca5ac04477fdff50ed84c80\"},\"description\":\"This paper concerns the problem of determining optimal placement of rectangular blocks within a rectangular area known as the packing or cutting-stock problem. 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