Computing k-Modal Embeddings of Planar Digraphs

Given a planar digraph G and a positive even integer k, an embedding of G in the plane is k-modal, if every vertex of G is incident to at most k pairs of consecutive edges with opposite orientations, i.e., the incoming and the outgoing edges at each vertex are grouped by the embedding into at most k sets of consecutive edges with the same orientation. In this paper, we study the k-Modality problem, which asks for the existence of a k-modal embedding of a planar digraph. This combinatorial problem is at the very core of a variety of constrained embedding questions for planar digraphs and flat clustered networks. First, since the 2-Modality problem can be easily solved in linear time, we consider the general k-Modality problem for any value of k>2 and show that the problem is NP-complete for planar digraphs of maximum degree Delta <= k+3. We relate its computational complexity to that of two notions of planarity for flat clustered networks: Planar Intersection-Link and Planar NodeTrix representations. This allows us to answer in the strongest possible way an open question by Di Giacomo [https://doi.org/10.1007/978-3-319-73915-1_37], concerning the complexity of constructing planar NodeTrix representations of flat clustered networks with small clusters, and to address a research question by Angelini et al. [https://doi.org/10.7155/jgaa.00437], concerning intersection-link representations based on geometric objects that determine complex arrangements. On the positive side, we provide a simple FPT algorithm for partial 2-trees of arbitrary degree, whose running time is exponential in k and linear in the input size. Second, motivated by the recently-introduced planar L-drawings of planar digraphs [https://doi.org/10.1007/978-3-319-73915-1_36], which require the computation of a 4-modal embedding, we focus our attention on k=4. On the algorithmic side, we show a complexity dichotomy for the 4-Modality problem with respect to Delta, by providing a linear-time algorithm for planar digraphs with Delta <= 6. This algorithmic result is based on decomposing the input digraph into its blocks via BC-trees and each of these blocks into its triconnected components via SPQR-trees. In particular, we are able to show that the constraints imposed on the embedding by the rigid triconnected components can be tackled by means of a small set of reduction rules and discover that the algorithmic core of the problem lies in special instances of NAESAT, which we prove to be always NAE-satisfiable - a result of independent interest that improves on Porschen et al. [https://doi.org/10.1007/978-3-540-24605-3_14]. Finally, on the combinatorial side, we consider outerplanar digraphs and show that any such a digraph always admits a k-modal embedding with k=4 and that this value of k is best possible for the digraphs in this family

Circum-Navigating The World Island, Among Enemies

Everyday our vision travels across time and space. We see images in the media about atrocities, disruptions, crises, famine, and wars. And in each case, our sense of injustice is awakened. We feel outrage and indignation based upon our ideals and value systems, which were formed through our traditions and religions. But in this age where the power of media and information is so powerful, what we see is often manufactured to appeal to our values. While these values circulate among the images we see in cyberspace, these manipulations are rooted in certain realities: geography, natural resources, and power relationships. Our values are managed to serve the control of resources and territory. They serve the deeper reality of geography and geopolitics. How then are these ideals and values created, manipulated, and opposed across various pivots or boundaries, between East and West, between the individual and the collective? Through English geographer Sir Halford Mackinder’s concepts of “pivot” and “heartland”; German philosopher Carl Schmitt’s importance of “nomos”; and French writer Victor Segalen’s reflections on the loss of cultural diversity, we outline this priority of geography. By examining these writers, we can begin to ask if our ideals and values have any real moral or theological significance, or if they are merely effects of the competition between powers. Can ideals and values lead to real change and development, or are they merely leashes to guide us based on the aims of power

GARUDA INDONESIA, REGISTERED TRADEMARK*

This essay examines the restrictions imposed on the use of images. It contrasts forms of transmission of images with contemporary transmission. It begins by focusing on the traditional image of the Garuda or Krut, and its function as a royal and state symbol in South East Asia. It then moves on to examine the philosophy of intellectual property and the manner in which private factions claim a new forms of sovereignty through the restrictions associated with information and images. It finally examines the fragility of corporate sovereignty and the phenomena of intellectual piracy

Book Review

Vital Nourishment: Departing from HappinessFrançois JullienTranslated by Arthur GoldhammerNew York: Zone Books, 2007Reviewed by J. T. Giordan

Sacred Commodities

This presentation will examine the circulation of sacred images as commodities. In urban areas in Southeast Asia, the trade in images of Buddhist, Brahmanist and Animist deities in the form of amulets is very popular, as is the trade in these sacred images in the tourist trade. The traditional manner of approaching this phenomenon is to impose traditional academic theories of capitalist exchange, commodity fetishism or spiritual decay. But this approach condemns the negative aspects of this phenomenon without appreciating its more authentic aspects. This paper wishes to show how the religious “eclecticism” found in Southeast Asia, is also present in the trade of sacred commodities. The paradoxes present in the commodification of sacred images also provide them with a renewed possibility to contribute to types of cultural redemption

KINNARI: ON THE SPACE BETWEEN TRADITIONAL AND CORPORATE MYTH

We navigate within a landscape full of mythical images and icons which ask for our commitment or trust. These include both manufactured corporate myths whose aim is the circulation of commodities and capital, and traditional myths which lead us to a place beyond mere exchange value. This essay seeks to investigate how we can begin to disentangle the various myths which compete for our attention. It draws from the works of Hans Blumenberg and Georg Simmel and their ideas of “pregnance” and “value”. It uses the stories surrounding the Thai mythical creature – the Kinnari – to demonstrate how the richness of traditional myth, can provide reorientation for those of us lost in contemporary culture. The story of the Kinnari points to the very source of wealth, value and trust.

The Challenge of Faith Today

This past October, during the inter-term recess, the Philippine Province of the Society of Jesus ran a conscientization program for about 35 Jesuits. This program was part of the effort of the Province to implement its thrust for justice, a thrust very strong in the Church today. The conscientization program was geared for awakening, awakening us to the realities of life, especially life among the poor and the oppressed. We were divided into three groups. One group went to the mountains of Bukidnon in Mindanao to experience the life of the people there. The Jesuits who went there lived with the Jesuits who run the mission parishes in Bukidnon under the dynamic leadership of Bishop Francisco Claver, a Jesuit Bishop. A second group went to Negros to experience the life of the sugar workers. The Jesuits who went there came back very aware of the plight of the sugar workers and the oppression of the system there. A third group of which I was a member went to Tondo, to experience the life of the urban poor, in particular, the squatters of the North Harbor. In a land area roughly equal in size to the campus of the Ateneo de Manila, there are about 200,000 people struggling to live. Most of them come from the southern provinces. They come to Manila to get jobs. Most of their jobs are on the piers or in Divisoria, so living in Tondo is very convenient for them, putting them very near their source of work. It was quite an interesting experience for us. We lived in one room of the community center of Slip Zero, near the San Miguel glass factory, all seven of us. It was very difficult for us to adapt to the living conditions, very difficult. Yet, somehow we managed. We broke up into three groups: one group worked in Zoto, where there is a very active community organization; another group went to Barrio Magsaysay to see the situation there, and the third group of which I was a member went to Magsaysay Village where the P.I.M.E. fathers, an Italian missionary Institute, have a parish. Here I saw the Church more alive than I have seen it in many other places. Amidst the poverty, the disease, and the filth I saw a vibrant community centered around the Church, struggling against many difficulties both within and without. Here I saw a living Church; here I came to understand more fully what I have committed myself to; here I came to see the face of Jesus Christ redeeming the hearts of God\u27s people. There are many difficulties there yet, but something is happening. When the fathers first went there, there was only apathy and indifference. Before martial law there was on the average one murder a week, with intense block rivalry. At first, the people tried to get all they could off the fathers, playing on their sympathies. Hardly anyone came to Mass. But gradually trust was built up, things started happening. The fathers became very much a part of the people\u27s life, and the dynamic of involvement and concern started to grow. Now, the liturgy there on a Sunday is one of the finest I have experienced either here or in the States. The people sing out full throated, participate fully, and have truly become a worshipping community sharing their common difficulties and common struggles. I bring up the example of my experiences in Magsaysay Village because I want to make clear that for the Christian faith to be realized today, it must be realized in a living community, and this is what the Church is, or is supposed to be. But, isn\u27t this precisely the problem, the lack of a living community. Because there is this lack of a living community, there is a weakening of our faith. We all know how difficult community is to achieve. Even those of us who are in religious life where our very existence is community centered know how difficult it is to form a good community. There are so many things in our human nature that work against community. There is a real alienation in our lives

On infinite tensor products of factors of type I2

It is proved, using Krieger's theorem, that ITPFI's of bounded type are ITPFI2. This answers a question asked by E. J. Wood