We present dynamic flow algorithms to solve the k-sink problem whose aim is to locate k sinks (evacuation centers) in such a way that the evacuation time of the last evacuee is minimized. In the confluent model, the evacuees originating from or passing through a vertex must evacuate to the same sink, and most known results on the k-sink problem adopt the confluent model. When the edge capacities are uniform (resp. general), our algorithms for non-confluent flow in the path networks run in O(n + k² log² n) (resp. O(n log(n) + k² log⁵ n)) time, where n is the number of vertices. Our algorithms for cycle networks run in O(k²n log² n) (resp. O(k²n log⁵ n)) time, when the edge capacities are uniform (resp. general).

Evacuation in emergency situations can be modeled by a dynamic flow network. Two criteria have been used before: one is the evacuation completion time and the other is the aggregate evacuation time of individual evacuees. The aim of this paper is to optimize the aggregate evacuation time in the simplest case, where the network is a path and only one evacuation center (called a sink) is to be introduced. The evacuees are initially located at the vertices, but their precise numbers are unknown, and are given by upper and lower bounds. Under this assumption, we compute the sink location that minimizes the maximum "regret." We present an $O(n^2\log n)$ time algorithm to solve this problem, improving upon the previously fastest $O(n^3)$ time algorithm, where $n$ is the number of vertices.

An arbitrary m×n Boolean matrix M can be decomposed exactly as M = UοV, where U (resp. V) is an m×k (resp. k ×n) Boolean matrix and ο denotes the Boolean matrix multiplication operator. We first prove an exact formula for the Boolean matrix J such that M = MοJT holds, where J is maximal in the sense that if any 0 element in J is changed to a 1 then this equality no longer holds. Since minimizing k is NP-hard, we propose two heuristic algorithms for finding suboptimal but good decomposition. We measure the performance (in minimizing k) of our algorithms on several real datasets in comparison with other representative heuristic algorithms for Boolean matrix decomposition (BMD). The results on some popular benchmark datasets demonstrate that one of our proposed algorithms performs as well or better on most of them. Our algorithms have a number of other advantages: They are based on exact mathematical formula, which can be interpreted intuitively. They can be used for approximation as well with competitive “coverage.” Last but not least, they also run very fast. Due to interpretability issues in data mining, we impose the condition, called the “column use condition,” that the columns of the factor matrix U must form a subset of the columns of M. In educational databases, the “ideal item response matrix” R, the “knowledge state matrix” A and the “Q-matrix” Q play important roles. We show that they are related exactly by R̅ = A ̅ο QT. Thus, given R, we can find A and Q with a small number (k) of “knowledge states,” using our exact BMD heuristics.

We study the surveillance of a polygonal area by a robot, which is equipped with a flashlight and moves along the polygon boundary. Its aim is to illuminate any intruder who can move faster than the moving flashlight beam, trying to avoid detection. We propose an O(n)-time algorithm for testing if it is possible for such a robot to always detect any intruder in a given polygon, where n is the number of vertices of the given polygon. This improves upon the best previous time complexity of O(n log n).

A room is a simple polygon with a prespecified point, called the door, on its boundary. Search starts at the door, and must detect all intruders that may be in the room, while making sure that no intruder escapes through the door during the search. Depending on where the door is placed, the intruders may be able to avoid detection. We present an efficient algorithm that can determine all the intervals on the boundary where the door should be placed in order for the polygon to be searchable by two guards on the boundary who keep mutual visibility, or a single searcher with a flashlight. Our algorithm works in O(n log n) time, where n is the number of vertices of the given polygon

Polygon search is the problem of finding mobile intruders who move unpredictably in a polygonal region. In this paper, we consider a special case of this problem, called boundary search, where the searcher is allowed to move only along the boundary of the polygon. We concentrate on a single searcher with one flashlight (called a 1-searcher), but it is known that a single boundary 1-searcher has the same searching power as a single boundary searcher with 360/spl deg/ vision. Our main result is that the movement of the searcher can be controlled by a finite-state machine having only seven states. This automaton has no built-in information about the input polygon and, for any given polygon P, if P can be searched by a boundary searcher at all, then this automaton will successfully search P, no matter where on the boundary of P it is initially placed. All information about P is acquired by the automaton online, as it searches P. We also show that if P can be searched by a boundary searcher, then our automaton searches it by circling its boundary less than three times.

The concept of k-coterie is useful for achieving k-mutual exclusion in distributed systems. A graph is said to be well covered if any of its maximal independent sets is also maximum. We first show that a graph G is well covered with independence number k if and only if G represents the incidence relation among quorums forming a k-coterie. We then discuss the problem of constructing k-coteries having some desirable properties. We also characterize the well-covered graphs with independence number 2. © 1999 John Wiley & Sons, Inc. Networks 34: 221–228, 1999

In the networks considered in this paper, processors do not have distinct identity numbers. On such a network, we discuss the leader election problem and the problem of counting the number of processors having the same identity number. As the communication mode, we consider port-to-port, broadcast-to-port, port-to-mail box, and broadcast-to-mailbox. For each of the above communication modes, we present: an algorithm for counting the number of processors with the same identity number; an algorithm for solving the leader election problem; and a graph theoretical characterization of the solvable class for the leader election problem.

In anonymous networks, the processors do not have identity numbers. We investigate the following representative problems on anonymous networks: (a) the leader election problem, (b) the edge election problem, (c) the spanning tree construction problem, and (d) the topology recognition problem. On a given network, the above problems may or may not be solvable, depending on the amount of information about the attributes of the network made available to the processors. Some possibilities are: (1) no network attribute information at all is available, (2) an upper bound on the number of processors in the network is available, (3) the exact number of processors in the network is available, and (4) the topology of the network is available. In terms of a new graph property called "symmetricity", in each of the four cases (1)-(4) above, we characterize the class of networks on which each of the four problems (a)(d) is solvable. We then relate the symmetricity of a network to its 1- and 2-factors.

For pt I see ibid. In anonymous networks, the processors do not have identity numbers. In Part I of this paper, we characterized the classes of networks on which some representative distributed computation problems are solvable under different conditions. A new graph property called symmetricity played a central role in our analysis of anonymous networks. In Part II, we turn our attention to the computational complexity issues. We first discuss the complexity of determining the symmetricity of a given graph, and then that of testing membership in each of the 16 classes of anonymous networks defined in Part I. It turns out that, depending on the class, the complexity varies from P-time to NP-complete or co-NP-complete.

Consider a computer system in which different types of serially reusable resources are shared by several classes of processes. We assume that each process in a process class has the same known maximum claim (i.e., the maximum resource requirement), but that the actual sequence of requests is unknown. Our resource manager uses the "expedient policy" in granting requests for resources, under the constraint that at most K (a constant) processes can reside in the system at any time.

Consider a network which can be represented by an acyclic directed graph such that the links represented by the edges are subject to failure. Under the assumption that at most one link can fail at any time, we want to locate a failed link, if any, by means of certain tests. A test is performed by injecting a signal at a vertex and monitoring it at another vertex and can reveal if there is a failed link on any path between the two vertices. We want to find a minimal set of tests that can uniquely locate any single fault. Since this problem is in general NP-complete, we investigate a special case where the given network has a tree structure. We present an algorithm whose worst case running time can be bounded by a linear function of the input size.

Two of the three authors who did the first extensive work on 2-way pushdown automata [1] consider multitape and multihead extensions of 1-way and 2-way deterministic and nondeterministic pushdown automata (PDA).

Yeh (Information and Control, vol. 13, pp. 140–155, 1968). The concepts of homomorphism and substitution property have played an important role in the structure theory of complete deterministic automata. In this paper the author tries to extend them to the general case of incomplete nondeterministic automata.1

The aim of this paper is to obtain a procedure for finding a minimum state nondeterministic finite automaton (NDA) equivalent to a given (in general, nondeterministic) finite automaton. Given a finite automaton A, we derive from A a matrix of 1' s and 0's, called a reduced automaton matrix RAM) of A, in a certain way and show that each state of A corresponds to a grid over the RAM. A grid consists of a set of rows and a set of columns of an RAM such that only 1's appear at the intersections. It is also shown that the union of all the grids, each of which corresponds to a state of A, covers all the 1 entries of an RAM.