師海忠(Haizhong Shi)，男，甘肅臨洮人，運籌學與控制論專業理學博士，教授。
基本介紹
- 中文名：師海忠
- 畢業院校：中國科學院
- 學位/學歷：博士
- 專業方向：運籌學與控制論
教育經歷,工作經歷,教學成果,科研成果,研究方向,提出猜想,解決的問題,
教育經歷
1986年6月於蘭州大學數學力學系畢業，獲理學學士學位。
1992年6月於蘭州大學數學系獲理學碩士學位。
1998年6月於中國科學院套用數學研究所獲運籌學與控制論專業理學博士學位（導師：堵丁柱教授）。
工作經歷
1986年7月至1995年8月在西北師範大學數學系任助教、講師。
1998年7月至2012年8月在西北師範大學計算機科學系任副教授、教授。
2012年9月至今在西北師範大學數學與統計學院任教授。
教學成果
1.給計算機科學系本科生講授課程：軟體工程、作業系統、計算機網路、程式設計（Pascal語言、C語言）、離散數學、機率論與數理統計、線性代數。
2.給數學系本科生講授高等代數、運籌學、抽象代數。
3.2012年提出並創建了西北師範大學計算機科學系本科軟體工程專業。
4.指導本科生參加全國大學生數學建模競賽，獲得全國二等獎一項、省級特等獎兩項；指導碩士研究生參加全國研究生數學建模競賽。獲得三等獎三項。
科研成果
1.1設計出超級計算機互連網路的多種模型
a)互連網路的代數環模型
b)互連網路的向量圖模型
c)正則圖連通圈網路：多種模型的統一體
d)互連網路的新模型：多部群論模型
e)互連網路的層次環群論模型
f)互連網路的k層次環r乘圖模型
g)互連網路的細胞分裂生長圖模型
1.2設計出的典型互連網路結構（部分）
a)交叉立方體連通圈網路
b)Mobius立方體連通圈網路
c)摺疊立方體連通圈網路
d)(n, k) – 多部星網路
e)(n, k) – 多部冒泡排序網路
f)(n, k) – 多部修正冒泡排序網路
研究方向
1(V, R) – 半群
1.1 圖半群理論及套用
1.1.1 互連網路半群
1.1.2 複雜網路半群
1.1.3 網際網路（Internet）半群
1.2 有向圖半群理論及套用
1.3 超圖半群理論及套用
1.4 隨機圖半群理論及套用
1.5 (V,R)-半群理論及套用
2 (V,R)-語言
2.1 無向圖語言
2.2 有向圖語言
2.3 超圖語言
2.4 隨機圖語言
2.5 (V,R)-語言
3 自然語言的有向圖模型
3.1 單詞有向圖
3.2 句子有向圖
3.3 段落有向圖
3.4 文章有向圖
4 正則圖連通圈網路理論及套用
5 環圖理論及套用
6 向量圖和有向向量圖理論及套用
7 細胞分裂生長圖理論及套用
提出猜想
1 關於超級計算機互連網路的猜想
猜想 設G=(V,E)是具有頂點集V={1,2,…,n}(n>2)和m條邊的連通圖。如果m=2r，則由G生成的Cayley圖是邊不交的k(0<=k<=r)個Hamilton圈和m-2k個完美對集的並；如果m=2r+1，則由G生成的Cayley圖是邊不交的k(0<=k<=r)個Hamilton圈和m-2k個完美對集的並。
2關於(V,R)-半群與(V,R)-語言的猜想
猜想1.1：每個頂點數大於2的圖半群都是可重構的。猜想1.2：每個頂點數大於2的無向圖語言都是可重構的。 重構猜想：每個頂點數大於2的圖都是可重構的。以上三個猜想是相互等價的。
猜想2.1：每個4正則簡單圖半群都包含3正則子圖半群。猜想2.2：每個4正則簡單無向圖語言都包含3正則無向子圖語言。
猜想3.1：若k>2,則不存在每對頂點均由唯一的長為k的路元連線起來的圖半群。猜想3.2：若k>2,則不存在每對頂點均由唯一的長為k的路字連線起來的無向圖語言。
猜想4.1: 每個連通圖半群的邊集均為最多(v+1)/2(取整)個邊不重路半群的邊集的並。
猜想4.2: 每個連通無向圖語言的邊集均為最多(v+1)/2(取整)個邊不重無向路語言的邊集的並。
猜想5.1： 每個2邊連通的簡單圖半群的邊集均為v-1個圈半群的邊集的並集。猜想5.2： 每個2邊連通的無向簡單圖語言的邊集均為v-1個無向圈語言的邊集的並集。
猜想6.1：若圖半群是簡單塊半群，且至少有v/2+k個度不小於k的頂點，則該圖半群有長至少為2k的圈元。猜想6.2：若無向圖語言是簡單塊語言，且至少有v/2+k個度不小於k的頂點，則該無向圖語言有長至少為2k的圈字。
問題7.1: 設f(n)是有n個頂點的不含有3正則子圖半群的簡單圖半群的最大可能邊數，確定f(n). 問題 7.2: 設f(n)是有n個頂點的不含有3正則無向子圖語言的簡單無向圖語言的最大可能邊數，確定f(n).
猜想8.1：|E|>|V|(k-1)/2的簡單圖半群一定包含具有k條邊的所有樹半群，其中，|E|和|V|分別表示該圖半群的邊數和頂點數。猜想8.2：|E|>|V|(k-1)/2的簡單無向圖語言一定包含具有k條邊的所有無向樹語言，其中，|E|和|V|分別表示該無向圖語言的邊數和頂點數。
解決的問題
1 師海忠等證明
(a)自然語言是有向圖語言
(b)有向圖語言是正則語言
(c)自然語言是正則語言
(d)英語、漢語等自然語言都是正則語言。
2師海忠的論文“互連網路的新模型：多部群論模型”解決了難題：如何提高星網路等互連網路的可擴展性？
3建立了自然語言的有向圖模型。
Representtative scientifitic research achievement
1 Models and structures of interconnection networks
1.1Models designed for interconnection networks of supercomputer
a)A ring-theoritic model for interconnection networks
b)A vector graph model for interconnection networks
c)Regular graph connected cycle: A unity model of many interconnection networks
d)New model for interconnection network: Multipartite group-theoretic model
e)A hierarchical ring group-theoretic model for interconnection network
f)A new model for interconnection network: k-hierarchical ring and r-layer graph networks
g)Cell-breeding graph model for interconnection network
1.2Classical structures designed for interconnection nework
a)Crossed cube connected cycle networks
b)Mobius cube connected cycle networks
c)Folded hypercube connected cycle networks
d)(n,k)-multipartite star networks
e)(n,k)-multipartite bubblesort networks
f)(n,k)-multipartite modified bubblesort networks
2Developed research fields
2.1(V,R)-semigroup
2.1.1 Graph semigroup theory with applications
2.1.1.1Interconnection network semigroup
2.1.1.2Complex network semigroup
2.1.1.3Internet semigroup
2.1.2 Digraph semigroup theory with applications
2.1.3 Hypergraph semigroup theory with applications
2.1.4 Random graph semigroup theory with applications
2.1.5 (V,R)-semigoup theory with applications
2.2 (V,R)-language
2.2.1 Undirected graph language
2.2.2 Digraph language
2.2.3 Hypergraph language
2.2.4 Random language
2.2.5 (V,R)-language
2.3 Digraph models for nature languages
2.3.1 Word digraph
2.3.2 Sentence digraph
2.3.3 Passage digraph
2.3.4 Article digraph
2.4 Regular graph connected cycle network theory with applications
2.5 Ring graph theory with applications
2.6 Vector graph and vector digraph theory with applications
2.7 Cell-breeding graph theory with applications
3 Proposed conjectures
3.1 Proposed conjecture for interconnection network
Conjecture Let G=(V,E) be a connected graph with node set {1,2,…,n} (n>2) and m edges. If m=2r, then the Cayley graph generated by G is the union of k (0<=k<=r) edge-disjoint Hamiltonian cycles and m-2k perfected matchings; if m=2r+1, then the Cayley graph generated by G is the union of k (0<=k<=r) edge-disjoint Hamiltonian cycles and m-2k perfected matchings.
3.2 Proposed conjectures for (V,R)-semigoup and (V,R)-language
Conjecture 1.1: every graph-semigroup with v>2 is reconstructible.
Conjecture 1.2: every undirected graph language with v>2 is reconstructible. Conjecture1.1, Conjecture1.2 and Reconstruction conjecture are equivalent.
Conjecture 2.1: Every 4-regular simple graph-semigroup contains a 3-regular subgraph-semigroup.
Conjecture 2.2: Every 4-regular simple undirected graph language contains a 3-regular undirected subgraph language.
Conjecture 3.1: If k>2, then there exists no graph-semigroup with the property that every pair nodes is connected by a unique path element of length k.
Conjecture 3.2: If k>2, then there exists no undirected graph language with the property that every pair nodes is connected by a unique path word of length k.
Conjecture 4.1: The edge set of every connected graph-semigroup is the union of at most (v+1)/2 (integer) edge sets of edge-disjoint path-semigroups.
Conjecture 4.2: The edge set of every undirected connected graph language is the union of at most (v+1)/2 (integer) edge sets of edge-disjoint undirected path languages.
Conjecture 5.1: The edge set of every 2-edge-connected simple graph-semigroup is the union of v-1 edge sets of cycle-semigroups.
Conjecture 5.2: The edge set of every undirected 2-edge-connected simple graph language is the union of v-1 edge sets of undirected cycle languages.
Conjecture 6.1: If graph-semigroup is a simple block semigroup with at least v/2+k vertices of degree at least k, then the graph-semigroup has a cycle element of length at least 2k.
Conjecture 6.2: If undirected graph language is a simple block language with at least v/2+k vertices of degree at least k, then the undirected graph language has a cycle word of length at least 2k.
Problem 7.1: Let f(n) be the maximum possible number of edges in a simple graph-semigroup on n vertices which contains no 3-regular subgraph semigroup. Determine f(n).
Problem 7.2: Let f(n) be the maximum possible number of edges in a simple undirected graph language on n vertices which contains no 3-regular undirected subgraph language. Determine f(n).
Conjecture 8.1: A simple graph-semigroup with |E|>|V|(k-1)/2 must contains every tree semigroup with k edges, where |E| and |V| are number of vertices and number of edges of the graph-semigroup.
Conjecture 8.2: A simple undirected graph language with |E|>|V|(k-1)/2 must contains every undirected tree languages with k edges, where |E| and |V| are number of vertices and number of edges of the undirected graph language.
4 Solved problems
4.1 Haizhong Shi, etc, proved:
a) Any nature language is a digraph language;
b) Any Digraph language is a regular language;
c) Any nature language is a regular language;
d) English, Chinese, etc, are all regular languages
4.2 In paper “A new model for interconnection network: Multipartite group-theoretic model”, Haizhong Shi solved the problem: how to improve the scalability of certain interconnection networks, such as star netwrok, etc.?
4.3 Establish digraph models of Nature languages
