For an edge-weighted graph G with n vertices and m edges, the minimum k-way cut problem is to nd a partition of the vertex set into k non-empty subsets so that the weight sum of edges between di erent subsets is minimized. For this problem with k = 5 and 6, we present a deterministic algorithm that runs in O(n k 2 (nF (n;m)+C 2 (n;m)+n 2 )) = O(mn k log(n 2 =m)) time, where F (n;m) and C 2 (n;m...

We present several simple probabilistic data structures for implementing priority queues. We present a data structure called simple bottom-up sampled heap (SBSH), supporting insert in O(1) expected time and delete, delete minimum, decrease key and meld in O(log n) time with high probability. An extension of SBSH called BSH1, supporting insert and meld in O(1) worst case time is presented. This ...

Let A and B be two sets of m resp. n weighted points in the plane, with m ≤ n. We present (1 + 6) and (2+6)-approximation algorithms for the minimum Euclidean Earth Mover’s Distance between A and B under translations and rigid motions respectively. In the general case where the sets have unequal total weights the algorithms run in O((nm/6) log(n/6)) time for translations and O((nm/6) log(n/6)) ...

In the structure of the title salt, 2C(7)H(10)N(+)·C(8)H(2)Cl(2)O(4) (2-)·H(2)O, the two benzyl-aminium anions have different conformations, one being essentially planar and the other having the side chain rotated out of the benzene plane [minimum ring to side-chain C-C-C-N torsion angles = -3.6 (6) and 50.1 (5)°, respectively]. In the 4,5-dichloro-phthalate dianion, the carboxyl-ate groups mak...

Given an undirected graph representing of processors, and a source node containing a network a message that must be broadcast to all the nodes, find a scheme that accomplishes the broadcast in the minimum number of time steps. A t each time step, any processor that has received the message is allowed t o communicate the message to at most one of its neighbors in the network, i.e. can communicat...

Structure isomers of the Au(10)(-) cluster and their chemical reactivity with O(2) are studied using photoelectron spectroscopy under different experimental conditions. In addition to the global minimum triangular D(3h) structure, at least three low-lying isomers (X', X'', and X''') are observed distinctly using argon tagging and O(2) titration. The D(3h) structure has a very high electron affi...

We present the first polynomial time algorithms for solving the NPcomplete graph problems DOMINATING SET and TOTAL DOMINATING SET when restricted to asteroidal triple-free graphs. We also present algorithms to compute a minimum cardinality dominating set and a minimum cardinality total dominating set on a large superclass of the asteroidal triple-free graphs, called DDP-graphs. These algorithms...

In the minimum sum coloring problem, the goal is to color the vertices of a graph with the positive integers such that the sum of all colors is minimal. Recently, it was shown that coloring a graph by iteratively coloring maximum independent sets yields a 4 + o(1) approximation for the minimum sum coloring problem. In this note, we show that this bound is tight. We construct a graph for which t...

In this paper we suggest new scaling algorithms for the assignment and minimum mean cycle problems. Our assignment algorithm is based on applying scaling to a hybrid version of the recent auction algorithm of Bertsekas and the successive shortest path algorithm. The algorithm proceeds by relaxing the optimality conditions, and the amount of relaxation is successively reduced to zero. On a netwo...

Given an N x N array of OS and Is, the closest pair problem is to determine the minimum distance between any pair of ones. Let D be this minimum distance (or D = 2N if there are fewer than two Is). Two solutions to this problem are given, one requiring O(log( N) + D) time and the other O(log( N)). These solutions are for two types of parallel computers arranged in a pyramid fashion with the bas...