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2007.01.08

ALENEXとSODA

ALENEXでの発表も無事終わり、今は発表聞いたり、部屋で修論を書くべく悶絶していたり街をぶらぶらしたりしてます。
今、ニューオリンズでは数学の学会もあって5000人ぐらいの数学者が街にいるらしい。

発表聞いたり予稿集をざっと読んだところで(僕が)面白そうな話
Faster Filters for Approximate String Matching [pdf]
近似マッチングにインデクスを使って候補を絞るものでsuffix filters (suffix arrays/treesを内部で使う)を提案

A Near-Optimal Algorithm for Computing the Entropy of a Stream [pdf]
ストリーム問題(データを全部同時に見れない、メモリに一部分しかのらない)でデータのエントロピーの近似を求める

Ultra-succinct Representaiton of Ordered Trees [pdf]
順序木の最新版。ほぼ全ての操作を実装。さらにtypicalな木に対してさらに小さくなる(nノードの2分木はn bitで表現可能)

Making Deterministic Signatures Quickly
S⊂Uに対して、各Sの要素から|U| >> |T| となるようなT上への単射を求めるdeterministicな方法を提案。これを再帰的に適用するとSから|T'|=O(log|S|)までの単射が求まりsignatureとかに使える。best student paper

Succinct Indexes for Strings, Binary Relations and Multi-labeled Trees [pdf]
圧縮索引は索引とデータが密に結合している場合が多いが索引だけを別に持つことを提案。データの方が自由にencodeできて、瞬時復元可能なデータ構造とかを使える

A Simple Storage Scheme for Strings Achieving Entropy Bounds
圧縮したまま好きな場所のデータをO(logn) bit 分瞬時復元可能なデータ構造をテーブルと符号化だけでする。BWTした後のデータを提案方法で符号化した場合の解析もある

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