We describe a new tool for curriculum design. By carefully choosing two traditional course subjec... more We describe a new tool for curriculum design. By carefully choosing two traditional course subject areas that have a disciplinary thread in common, trimming both to their essential core topics using program outcomes as a guide, then combining the results, we create an “intracourse.” We give criteria for evaluating potential intracourse constituent pairs. We discuss alternative approaches to realizing the combination. Intracourses can be used to address several difficult curriculum design challenges. Rapid technological advances routinely create demands for new technical competencies within fixed engineering curriculum boundaries. Current trends toward increasing general education requirements reduce available time and other resources for specialized engineering courses. Intracourses allow for novel new curriculum design solutions in such constrained environments. Each intracourse also provides engineering students with direct experience in exploring the boundary between two traditio...
Cyber has permeated all aspects of our lives and society. Consequently, it is a moral imperative ... more Cyber has permeated all aspects of our lives and society. Consequently, it is a moral imperative that cyber be integrated into all levels of education. This paper provides a multi-level, multidisciplinary approach for holistically integrating cyber into a student’s academic experience. Our approach suggests formally integrating cyber throughout an institution’s curriculum, including within the required general education program, in electives from a variety of disciplines, as multi-course threads, as minors, and in numerous cyber-related majors. Our holistic approach complements in-class curricula with both a pervasive cyber-aware environment and experiential, outside-the-classroom activities that apply concepts and skills in realworld environments. The goal of our approach is to provide all educated individuals a level of cyber education appropriate for their role in society. Throughout the description of our approach, we include examples of its implementation at the United States M...
ABSTRACT Given a graph G=(V,E), the problem of computing ε(G), the maximum efficiency of G, is th... more ABSTRACT Given a graph G=(V,E), the problem of computing ε(G), the maximum efficiency of G, is that of computing the maximum number of nodes in V−R, over all sets R⊆V, that are dominated by only one node in R. In “Efficient sets in graphs” by P.J. Bernhard a linear time algorithm that computes ε(G) when G is a tree is described. We show that a similar approach can be used to compute ε(G) when G is an AC graph.
Abstract. The graph search problem asks for a strategy that enables a minimum sized team of searc... more Abstract. The graph search problem asks for a strategy that enables a minimum sized team of searchers to capture a “fugitive ” while it evades and potentially multiplies through a network. It is motivated by the need to eliminate fast spreading viruses and other malicious software agents in computer networks. The current work improves on previous results with a self-stabilizing algorithm that clears an n node tree network using only 1+log n searchers and O(n log n) moves after initialization. Since Θ(log n) searchers are required to clear some tree networks even in the sequential case, this is the best that any self-stabilizing algorithm can do. The algorithm is based on a novel multi-layer traversal of the network. 1
Abstract. The disjoint-set data structure is used to maintain a collection of non-overlapping set... more Abstract. The disjoint-set data structure is used to maintain a collection of non-overlapping sets of elements from a finite universe. Algorithms that operate on this data structure are often referred to as Union-Find algorithms. They are used in numerous practical applications and are also available in several software libraries. This paper presents an extensive experimental study comparing the time required to execute 55 variations of Union-Find algorithms. The study includes all the classical algorithms, several recently suggested enhancements, and also different combinations and optimizations of these. Our results clearly show that a somewhat forgotten simple algorithm developed by Rem in 1976 is the fastest, in spite of the fact that its worst-case time complexity is inferior to that of the commonly accepted “best ” algorithms. Keywords: Union-Find, Disjoint Set, Experimental Algorithms. 1
We introduce a k-response set as a set of vertices where responders can be placed so that given a... more We introduce a k-response set as a set of vertices where responders can be placed so that given any set of k emergencies, these responders can respond, one per emergency, where each responder covers its own vertex and its neighbors. A weak k-response set does not have to worry about emergencies at the vertices of the set. We define Rk and rk as the minimum cardinality of such sets. We provide bounds on these parameters and discuss connections with domination invariants. For example, for a graph G of order n and minimum degree at least 2, R2(G) ≤ 2n/3, while r2(G) ≤ n/2 provided G is also connected and not K3. We also provide bounds for trees T of order n. We observe that there are for each k trees for which rk(T) ≤ n/2, but that the minimum Rk(T) appears to grows with k; a novel computer algorithm is used to show that R3(T)> n/2. As expected, these parameters are NP-hard to compute, and we provide a linear-time algorithm for trees for fixed k.
We determine the maximum number of edges that a chordal graph G can have if its degree, ∆(G), and... more We determine the maximum number of edges that a chordal graph G can have if its degree, ∆(G), and its matching number, ν(G), are bounded. To do so, we show that for every d, ν ∈ N, there exists a chordal graph G with ∆(G) < d and ν(G) < ν whose number of edges matches the upper bound, while having a simple structure: it is a disjoint union of cliques and stars.
A de-pair (ode-pair) in a graph consists of two disjoint subsets of vertices with the same closed... more A de-pair (ode-pair) in a graph consists of two disjoint subsets of vertices with the same closed neighborhood (open neighborhood). We consider the question of determining the smallest and largest subsets over all such pairs. We provide sharp bounds on these for general graphs and for trees, and show that the associated parameters are computable for trees but intractable in general.
In this paper we consider 1-movable dominating sets, motivated by the use of sensors employed to ... more In this paper we consider 1-movable dominating sets, motivated by the use of sensors employed to detect certain events in networks, where the sensors have a limited ability to react under changing conditions in the network. A 1-movable dominating set is a dominating set S ⊆ V (G) such that for every v ∈ S, either S − {v} is a dominating set, or there exists a vertex u ∈ (V (G) − S) ∩ N(v) such that (S − {v}) ∪ {u} is a dominating set. We present computational complexity results and bounds on the size of 1-movable dominating sets in arbitrary graphs. We also give a polynomial time algorithm to find minimum 1-movable dominating sets for trees. We conclude by extending this idea to k-movable dominating sets.
Broadcast domination assigns an integer value f(u) 0 to each vertex u of a given graph, such that... more Broadcast domination assigns an integer value f(u) 0 to each vertex u of a given graph, such that every vertex u with f(u) = 0 is within distance f(v) from a vertex v with f(v) > 0. We can regard the vertices v with f(v) > 0 as broadcast stations, each having a transmission power that might be di erent from the powers of other stations. The optimal broadcast domination problem seeks to minimize the sum of the costs of the broadcasts assigned to the vertices of the graph. We present dynamic programming algorithms that solve the optimal broadcast domination problem for the rst classes of graphs with non-trivial solutions: interval graphs, series-parallel graphs, and trees. We also show that optimal broadcast domination is equivalent to optimal domination on proper interval graphs.
We describe a new tool for curriculum design. By carefully choosing two traditional course subjec... more We describe a new tool for curriculum design. By carefully choosing two traditional course subject areas that have a disciplinary thread in common, trimming both to their essential core topics using program outcomes as a guide, then combining the results, we create an “intracourse.” We give criteria for evaluating potential intracourse constituent pairs. We discuss alternative approaches to realizing the combination. Intracourses can be used to address several difficult curriculum design challenges. Rapid technological advances routinely create demands for new technical competencies within fixed engineering curriculum boundaries. Current trends toward increasing general education requirements reduce available time and other resources for specialized engineering courses. Intracourses allow for novel new curriculum design solutions in such constrained environments. Each intracourse also provides engineering students with direct experience in exploring the boundary between two traditio...
Cyber has permeated all aspects of our lives and society. Consequently, it is a moral imperative ... more Cyber has permeated all aspects of our lives and society. Consequently, it is a moral imperative that cyber be integrated into all levels of education. This paper provides a multi-level, multidisciplinary approach for holistically integrating cyber into a student’s academic experience. Our approach suggests formally integrating cyber throughout an institution’s curriculum, including within the required general education program, in electives from a variety of disciplines, as multi-course threads, as minors, and in numerous cyber-related majors. Our holistic approach complements in-class curricula with both a pervasive cyber-aware environment and experiential, outside-the-classroom activities that apply concepts and skills in realworld environments. The goal of our approach is to provide all educated individuals a level of cyber education appropriate for their role in society. Throughout the description of our approach, we include examples of its implementation at the United States M...
ABSTRACT Given a graph G=(V,E), the problem of computing ε(G), the maximum efficiency of G, is th... more ABSTRACT Given a graph G=(V,E), the problem of computing ε(G), the maximum efficiency of G, is that of computing the maximum number of nodes in V−R, over all sets R⊆V, that are dominated by only one node in R. In “Efficient sets in graphs” by P.J. Bernhard a linear time algorithm that computes ε(G) when G is a tree is described. We show that a similar approach can be used to compute ε(G) when G is an AC graph.
Abstract. The graph search problem asks for a strategy that enables a minimum sized team of searc... more Abstract. The graph search problem asks for a strategy that enables a minimum sized team of searchers to capture a “fugitive ” while it evades and potentially multiplies through a network. It is motivated by the need to eliminate fast spreading viruses and other malicious software agents in computer networks. The current work improves on previous results with a self-stabilizing algorithm that clears an n node tree network using only 1+log n searchers and O(n log n) moves after initialization. Since Θ(log n) searchers are required to clear some tree networks even in the sequential case, this is the best that any self-stabilizing algorithm can do. The algorithm is based on a novel multi-layer traversal of the network. 1
Abstract. The disjoint-set data structure is used to maintain a collection of non-overlapping set... more Abstract. The disjoint-set data structure is used to maintain a collection of non-overlapping sets of elements from a finite universe. Algorithms that operate on this data structure are often referred to as Union-Find algorithms. They are used in numerous practical applications and are also available in several software libraries. This paper presents an extensive experimental study comparing the time required to execute 55 variations of Union-Find algorithms. The study includes all the classical algorithms, several recently suggested enhancements, and also different combinations and optimizations of these. Our results clearly show that a somewhat forgotten simple algorithm developed by Rem in 1976 is the fastest, in spite of the fact that its worst-case time complexity is inferior to that of the commonly accepted “best ” algorithms. Keywords: Union-Find, Disjoint Set, Experimental Algorithms. 1
We introduce a k-response set as a set of vertices where responders can be placed so that given a... more We introduce a k-response set as a set of vertices where responders can be placed so that given any set of k emergencies, these responders can respond, one per emergency, where each responder covers its own vertex and its neighbors. A weak k-response set does not have to worry about emergencies at the vertices of the set. We define Rk and rk as the minimum cardinality of such sets. We provide bounds on these parameters and discuss connections with domination invariants. For example, for a graph G of order n and minimum degree at least 2, R2(G) ≤ 2n/3, while r2(G) ≤ n/2 provided G is also connected and not K3. We also provide bounds for trees T of order n. We observe that there are for each k trees for which rk(T) ≤ n/2, but that the minimum Rk(T) appears to grows with k; a novel computer algorithm is used to show that R3(T)> n/2. As expected, these parameters are NP-hard to compute, and we provide a linear-time algorithm for trees for fixed k.
We determine the maximum number of edges that a chordal graph G can have if its degree, ∆(G), and... more We determine the maximum number of edges that a chordal graph G can have if its degree, ∆(G), and its matching number, ν(G), are bounded. To do so, we show that for every d, ν ∈ N, there exists a chordal graph G with ∆(G) < d and ν(G) < ν whose number of edges matches the upper bound, while having a simple structure: it is a disjoint union of cliques and stars.
A de-pair (ode-pair) in a graph consists of two disjoint subsets of vertices with the same closed... more A de-pair (ode-pair) in a graph consists of two disjoint subsets of vertices with the same closed neighborhood (open neighborhood). We consider the question of determining the smallest and largest subsets over all such pairs. We provide sharp bounds on these for general graphs and for trees, and show that the associated parameters are computable for trees but intractable in general.
In this paper we consider 1-movable dominating sets, motivated by the use of sensors employed to ... more In this paper we consider 1-movable dominating sets, motivated by the use of sensors employed to detect certain events in networks, where the sensors have a limited ability to react under changing conditions in the network. A 1-movable dominating set is a dominating set S ⊆ V (G) such that for every v ∈ S, either S − {v} is a dominating set, or there exists a vertex u ∈ (V (G) − S) ∩ N(v) such that (S − {v}) ∪ {u} is a dominating set. We present computational complexity results and bounds on the size of 1-movable dominating sets in arbitrary graphs. We also give a polynomial time algorithm to find minimum 1-movable dominating sets for trees. We conclude by extending this idea to k-movable dominating sets.
Broadcast domination assigns an integer value f(u) 0 to each vertex u of a given graph, such that... more Broadcast domination assigns an integer value f(u) 0 to each vertex u of a given graph, such that every vertex u with f(u) = 0 is within distance f(v) from a vertex v with f(v) > 0. We can regard the vertices v with f(v) > 0 as broadcast stations, each having a transmission power that might be di erent from the powers of other stations. The optimal broadcast domination problem seeks to minimize the sum of the costs of the broadcasts assigned to the vertices of the graph. We present dynamic programming algorithms that solve the optimal broadcast domination problem for the rst classes of graphs with non-trivial solutions: interval graphs, series-parallel graphs, and trees. We also show that optimal broadcast domination is equivalent to optimal domination on proper interval graphs.
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Papers by Jean Blair