Coalition structure generation over graphs

We give the analysis of the computational complexity of coalition structure generation over graphs. Given an undirected graph G = (N,E) and a valuation function v : P(N) → R over the subsets of nodes, the problem is to find a partition of N into connected subsets, that maximises the sum of the components values. This problem is generally NP-complete; in particular, it is hard for a defined class of valuation functions which are independent of disconnected members — that is, two nodes have no effect on each others marginal contribution to their vertex separator. Nonetheless, for all such functions we provide bounds on the complexity of coalition structure generation over general and minor free graphs. Our proof is constructive and yields algorithms for solving corresponding instances of the problem. Furthermore, we derive linear time bounds for graphs of bounded treewidth. However, as we show, the problem remains NP-complete for planar graphs, and hence, for any Kk minor free graphs where k ≥ 5. Moreover, a 3-SAT problem with m clauses can be represented by a coalition structure generation problem over a planar graph with O(m2) nodes. Importantly, our hardness result holds for a particular subclass of valuation functions, termed edge sum, where the value of each subset of nodes is simply determined by the sum of given weights of the edges in the induced subgraph

Michigan Geology: A Bibliography, March 2016

The Michigan Geological Survey produced a historic Index of Michigan Geology with an extensive bibliography in 1956. This current bibliography is an update of the bibliography in the Martin and Straight compilation. It is not comprehensive, but provides a starting place for anyone interested in Michigan Geology. The Michigan Geological Survey plans to update this bibliography periodically with newly published citations as well as other older citations we find

The Wooster Voice (Wooster, Ohio), 1904-02-29, Hoover Cottage Edition

This edition of the voice is written by the women of Hoover Cottage - the first female dormitory at the College of Wooster. The college presents the Second Annual Minstrel Show to students and citizens of Wooster. The issue includes a program from said show. Wooster faculty grants permission for the basket ball team to make a trip to play Westminster and Grove City College. George Sherwood Eddy, seven years engaged in Y.M.C.A work in India, addresses the Student Christian Associations. Additionally, the issue includes a lengthy piece details the travels of Miss Gertrude Gingrich.https://openworks.wooster.edu/voice1901-1910/1054/thumbnail.jp

The Wooster Voice (Wooster, OH), 1994-04-08

New FYS system to be implemented in 1995, college faculty voted to have new First Year Seminar begin for the fall of 1995. Police find stolen goods in Richardson, Wooster police department find stolen goods in the college owned Richardson House. Allen, Kerr exhibit I.S. in Frick, Brant Allen and Anthony Kerr show their independent study at the Frick Art Museum.https://openworks.wooster.edu/voice1991-2000/1089/thumbnail.jp

The Wooster Voice (Wooster, OH), 1992-04-17

The Voice reviews the first incidence of Africa Week at the College. Senior Kevin Waugh passed away due to testicular cancer. Guest speaker Rhonda Rivera spoke on current gay and lesbian issues. Members of the International Students Association refute the statements made by their fellow member in the previous edition of the Voice. Students voice concern over lack of housing options. 1992 Independent Study conferences are listed. A large advertisement was placed encouraging upcoming graduates to buy Toyotas.https://openworks.wooster.edu/voice1991-2000/1038/thumbnail.jp

The Wooster Voice (Wooster, OH), 1942-09-24

This edition discusses the goals of the Big Four Financial Drive. There is a retelling of the fable The Ant and the Grasshopper which the author has titled Grasshopper Wins Again in Modern Fable of Japanese (Beetle) Menace. This version contains a bigoted view of Japanese Americans and refers to them as a racial slur. Additionally the issue highlights organizations such as the W.S.G.A., the M.S.G.A, Glee Club, drama, and varsity sports.https://openworks.wooster.edu/voice1941-1950/1041/thumbnail.jp

The Wooster Voice (Wooster, OH), 1997-02-21

In this edition of the Voice, SGA approves a resolution declaring the bagpipes a legitimate academically applied musical instrument. The Florence O. Wilson Bookstore phases out Greek Group apparel and supplies, sparking an outrage from Greek life members. In the Viewpoints section, a student responds to a previous week’s article on Valentine’s Day and romance. An article discusses the O.J. Simpson trial and verdict. As tradition, the “Betas” (Beta Kappa Phi), run naked through campus at 11:11pm on the coldest night of the year. Additionally, Patrick Hogan \u2797 paints a large and elaborate mural on the walls of his Bissman dorm room.https://openworks.wooster.edu/voice1991-2000/1164/thumbnail.jp